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Observation of Gravitational Waves from the Coalescence
of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration
ABSTRACT
We report the observation of a coalescing compact binary with component masses 2.5–4.5 M⊙
and 1.2–2.0 M⊙ (all measurements quoted at the 90% credible level). The gravitational-wave sig-
nal GW230529 181500 was observed during the fourth observing run of the LIGO–Virgo–KAGRA
detector network on 2023 May 29 by the LIGO Livingston observatory. The primary component of
the source has a mass less than 5 M⊙ at 99% credibility. We cannot definitively determine from
gravitational-wave data alone whether either component of the source is a neutron star or a black
hole. However, given existing estimates of the maximum neutron star mass, we find the most probable
interpretation of the source to be the coalescence of a neutron star with a black hole that has a mass
between the most massive neutron stars and the least massive black holes observed in the Galaxy. We
estimate a merger rate density of 55+127
−47 Gpc−3
yr−1
for compact binary coalescences with properties
similar to the source of GW230529 181500; assuming that the source is a neutron star–black hole
merger, GW230529 181500-like sources constitute about 60% of the total merger rate inferred for neu-
tron star–black hole coalescences. The discovery of this system implies an increase in the expected rate
of neutron star–black hole mergers with electromagnetic counterparts and provides further evidence
for compact objects existing within the purported lower mass gap.
Keywords: Gravitational wave astronomy(675) — Gravitational wave detectors(676) — Gravitational
wave sources(677) — Stellar mass black holes(1611) — Neutron stars(1108)
1. INTRODUCTION
In May 2023, the fourth observing run (O4) of the Ad-
vanced LIGO (Aasi et al. 2015), Advanced Virgo (Acer-
nese et al. 2015), and KAGRA (Somiya 2012; Aso et al.
2013) observatory network commenced following a series
of upgrades to increase the sensitivity of the network.
The prior three observing runs opened the field of ob-
servational gravitational-wave (GW) astronomy, with 90
probable compact binary coalescence (CBC) candidates
reported by the LIGO Scientific, Virgo, and KAGRA
Collaboration (LVK) at the conclusion of the third ob-
serving run (O3) (Abbott et al. 2023a) and further can-
didates found by external analyses (e.g., Nitz et al. 2023;
Mehta et al. 2023b; Wadekar et al. 2023). These in-
cluded the first observation of merging stellar-mass black
holes (Abbott et al. 2016a), the first observation of a
stellar-mass black hole merging with a neutron star (Ab-
bott et al. 2021a), and the first observation of two merg-
ing neutron stars (Abbott et al. 2017a). The first ob-
servation of two merging neutron stars was also a mul-
timessenger event accompanied by emission across the
electromagnetic (EM) spectrum (Abbott et al. 2017b;
Margutti & Chornock 2021). The continued discovery of
CBCs by the Advanced GW network in O4 and beyond
promises to reveal new information about the formation
pathways of compact binaries and the physics of their
evolution.
While GW observations have enabled detailed charac-
terization of the population of stellar-mass compact ob-
ject binary mergers overall (e.g., Abbott et al. 2023b),
the small number of observed mergers at the low-mass
end of the black hole mass spectrum leads to consider-
able uncertainty in this region of the mass distribution.
Dynamical mass measurements of X-ray binary systems
within the Milky Way suggest a paucity of compact ob-
jects with masses between ∼ 3–5 M⊙, and hence a lower
mass gap that divides the population of neutron stars
(with masses less than ∼ 3 M⊙; Rhoades & Ruffini 1974;
Kalogera & Baym 1996) and stellar-mass black holes
(observed to have masses above 5 M⊙; Bailyn et al.
1998; Ozel et al. 2010; Farr et al. 2011b). Although a
number of recent observations of non-interacting binary
2
systems (Thompson et al. 2019; Jayasinghe et al. 2021),
radio pulsar surveys (Barr et al. 2024), and GW obser-
vations (Abbott et al. 2020c, 2023b) have found hints
of compact objects residing in the lower mass gap, GW
observations have yet to quantify the extent and poten-
tial occupation of this gap (Fishbach et al. 2020; Farah
et al. 2022; Abbott et al. 2023b).
Here we report on the compact binary merger
signal GW230529 181500, henceforth abbreviated as
GW230529, which was detected by the LIGO Livingston
observatory on 2023 May 29 at 18:15:00 UTC; all other
observatories were either offline or did not have the sen-
sitivity required to observe this signal. We find that
the compact binary source of GW230529 had component
masses of 3.6+0.8
−1.2 M⊙ and 1.4+0.6
−0.2 M⊙ (all measurements
are reported as symmetric 90% credible intervals around
the median of the marginalized posterior distribution
with default uniform priors, unless otherwise specified).
Although we cannot definitively determine the nature
of the higher-mass (primary) compact object in the bi-
nary system, if we assume that all compact objects with
masses below current constraints on the maximum neu-
tron star mass are indeed neutron stars, the most prob-
able interpretation for the source of GW230529 is the
coalescence between a 2.5–4.5 M⊙ black hole and a neu-
tron star. GW230529 provides further evidence that a
population of compact objects exists with masses be-
tween the heaviest neutron stars and lightest black holes
observed in the Milky Way. Furthermore, if the source
of GW230529 was a merger between a neutron star and
a black hole, its masses are significantly more symmetric
than the neutron star–black holes (NSBHs) previously
observed via GWs (Abbott et al. 2023a), which increases
the expected rate of NSBHs that may be accompanied
by an EM counterpart.
We report on the status of the detector network at the
time of GW230529 in Section 2 and provide details of
the detection in Section 3. In Section 4 we present es-
timates of the source properties along with a discussion
of the inferred masses, spins, tidal effects, and consis-
tency of the signal with general relativity. We provide
updated constraints on merger rates and the inferred
properties of the compact binary and NSBH popula-
tions as well as population-informed posteriors on source
properties in Section 5. Section 6 provides analysis and
interpretation of the physical nature of the source com-
ponents. Implications for multimessenger astrophysics
and the formation of low-mass black holes are in Sec-
tions 7 and 8, respectively. Section 9 summarizes our
findings. Data from the analyses in this work are avail-
able on Zenodo (Abbott et al. 2024a).
2. OBSERVATORY STATUS AND DATA QUALITY
At the time of GW230529 (2023 May 29 18:15:00.7
UTC), LIGO Livingston was in observing mode; LIGO
Hanford was offline, having gone out of observing mode
one hour and thirty minutes prior to the detection. The
Virgo observatory was undergoing upgrades and was not
operational at the time of the detection. The KAGRA
observatory was in observing mode, but its sensitivity
was insufficient to impact the analysis of GW230529.
Hence, only the data from the LIGO Livingston obser-
vatory are used in the analysis of GW230529.
LIGO Livingston was observing with stable sensitiv-
ity for ≃ 66 hours up to and including the time of
the GW signal. At the time of the detection, the sky-
averaged binary neutron star (BNS) inspiral range was
≃ 150 Mpc. From the start of O4 until this event, the
LIGO Livingston BNS inspiral range (Chen et al. 2021a)
varied between 140–160 Mpc, a 4.5–19.4% increase com-
pared to the median BNS range in O3 (Buikema et al.
2020; Abbott et al. 2023a). Additional details on up-
grades to the LIGO observatories for O4 can be found
in Appendix A.
The Advanced LIGO observatories are laser interfer-
ometers that measure strain (Aasi et al. 2015). The ob-
servatories are calibrated via photon radiation pressure
actuation. An amplitude-modulated laser beam is di-
rected onto the end test masses inducing a known change
in the arm length from the equilibrium position (Karki
et al. 2016; Viets et al. 2018). For the strain data used
in the GW230529 analysis, the maximum 1σ bounds on
calibration uncertainties at LIGO Livingston were 6%
in amplitude and 6.5◦
in phase for the frequency range
20–2048 Hz.
Detection vetting procedures similar to those of past
GW candidates (Davis et al. 2021; Abbott et al. 2016b),
when applied to GW230529, find no evidence that in-
strumental or environmental artifacts (Helmling-Cornell
et al. 2023; Nguyen et al. 2021; Effler et al. 2015) could
have caused GW230529. We find no evidence of tran-
sient noise that is likely to impact the recovery of the
GW signal in the 256 s LIGO Livingston data segment
containing the signal.
3. DETECTION OF GW230529
GW230529 was initially detected in low latency in
data from the LIGO Livingston observatory. The sig-
nal was detected independently by three matched-filter
search pipelines: GstLAL (Messick et al. 2017; Sachdev
et al. 2019; Hanna et al. 2020; Cannon et al. 2021; Ew-
ing et al. 2023; Tsukada et al. 2023), MBTA (Adams
et al. 2016; Aubin et al. 2021) and PyCBC (Allen et al.
2012; Allen 2005; Dal Canton et al. 2021; Usman et al.
3
2016; Nitz et al. 2017; Davies et al. 2020). Although
GW230529 occurred when only a single detector was
observing, it was detected by all three pipelines with
high significance, and stands out from the background
distribution of noise triggers. More details are given in
Appendix B.
All three pipelines have a similar matched-filter-based
approach to identify GW candidates but differ in the
details of implementation. Each pipeline begins by per-
forming a matched-filtering analysis on the data from
the observatory with a bank of GW templates (Sakon
et al. 2024; Roy et al. 2019; Florian et al. 2024). Times
of high signal-to-noise ratio (S/N) are identified, after
which each pipeline performs its own set of signal con-
sistency tests, combines them with the S/N to make a
single ranking statistic for each candidate GW event,
and calculates a false alarm rate (FAR) by comparing
the ranking statistic of the candidate with the back-
ground distribution. The FAR is the expected rate of
triggers caused by noise with a ranking statistic greater
than or equal to that of the candidate.
For each pipeline, this procedure can be done in two
modes: a low-latency or online mode, and an offline
mode. In the online mode, the pipelines only use the
background information available at the time of a candi-
date to estimate its significance, along with low-latency
data-quality information. In the offline mode, pipelines
use more background information gathered from sub-
sequent observing times to estimate the significance of
candidates and use more refined data-quality informa-
tion. The offline mode enables more robust and repro-
ducible results at the cost of greater latency.
In both cases, the background distribution is extrap-
olated to higher significances. This enables the inverse
FAR to be greater than the time for which the back-
ground was collected. Pipelines have differing extrapo-
lation methods, and differing methods for calculating
the FAR of a single-detector GW candidates, details
of which can be found in Appendix C. These differ-
ing methods can cause the FARs reported by different
pipelines for the same candidate to vary to a signifi-
cant degree, as seen in the case of GW230529. How-
ever, all three pipelines recover a nearly identical S/N
for GW230529, as expected for an astrophysical signal
with a high match to the search templates. This, in con-
cert with the fact that the inverse FARs from the offline
analyses of all pipelines are much greater than the dura-
tion of the first half of the fourth observing run (O4a),
makes it highly likely that GW230529 is of astrophysi-
cal origin. Table 1 shows the online S/N, online inverse
FAR, and offline inverse FAR for each search pipeline.
Table 1. Properties of the detection of GW230529 from
each search pipeline. Significance is measured by the inverse
of the FAR.
GstLAL MBTA PyCBC
Online S/N 11.3 11.4 11.6
Online inverse FAR (yr) 1.1 1.1 160.4
Offline inverse FAR (yr) 60.3 >1000 >1000
4. SOURCE PROPERTIES
The source properties of GW230529 are inferred us-
ing a Bayesian analysis of the data from the LIGO Liv-
ingston observatory. We analyze 128 s of data including
frequencies in the range of 20–1792 Hz in the calculation
of the likelihood. To describe the detector noise, we as-
sume a noise power spectral density (PSD) given by the
median estimate provided by BayesWave (Littenberg
& Cornish 2015; Cornish & Littenberg 2015; Cornish
et al. 2021). We use the Bilby (Ashton et al. 2019;
Romero-Shaw et al. 2020) or Parallel Bilby (Smith
et al. 2020) inference libraries to generate samples from
the posterior distribution of the source parameters us-
ing a nested sampling (Skilling 2006) algorithm, as im-
plemented in the Dynesty software package (Speagle
2020).
Given the uncertain nature of the compact objects of
the source, we analyze GW230529 using a range of wave-
form models that incorporate a number of key physi-
cal effects. For our primary analysis, we employ binary
black hole (BBH) waveform models that include higher-
order multipole moments, the effects of spin-induced or-
bital precession, and allow for spin magnitudes on both
components up to the Kerr limit, but do not include
tidal effects on either component.
Systematic errors in inferred source properties due
to waveform modeling may be significant for NSBH
systems (Huang et al. 2021). We mitigate these ef-
fects by combining the posteriors inferred using two dif-
ferent signal models: the phenomenological frequency-
domain model IMRPhenomXPHM (Pratten et al.
2020; Garcı́a-Quirós et al. 2020; Pratten et al. 2021),
and a time-domain effective-one-body model SEOB-
NRv5PHM (Khalil et al. 2023; Pompili et al. 2023;
Ramos-Buades et al. 2023; van de Meent et al. 2023).
The posterior samples obtained independently using the
two signal models are broadly consistent. Unless other-
wise noted, we present results throughout this work ob-
tained by an equal-weight combination of the posterior
4
Table 2. Source properties of GW230529 from the pri-
mary combined analysis (BBH waveforms, high-spin, default
priors). We report the median values together with the
90% symmetric credible intervals at a reference frequency
of 20 Hz.
Primary mass m1/M⊙ 3.6+0.8
−1.2
Secondary mass m2/M⊙ 1.4+0.6
−0.2
Mass ratio q = m2/m1 0.39+0.41
−0.12
Total mass M/M⊙ 5.1+0.6
−0.6
Chirp mass M/M⊙ 1.94+0.04
−0.04
Detector-frame chirp mass (1 + z)M/M⊙ 2.026+0.002
−0.002
Primary spin magnitude χ1 0.44+0.40
−0.37
Effective inspiral-spin parameter χeff −0.10+0.12
−0.17
Effective precessing-spin parameter χp 0.40+0.39
−0.30
Luminosity distance DL/Mpc 201+102
−96
Source redshift z 0.04+0.02
−0.02
samples from both models under the default priors de-
scribed in Appendix D. Our measurements of key source
parameters for GW230529 are presented in Table 2.
Analysis details and results from other waveform mod-
els we consider are reported in Appendix D; we find
that the key conclusions of the analyses presented here
are not sensitive to the choice of signal model. In par-
ticular, the use of BBH models is validated by com-
parison to waveform models that include tidal effects,
finding no evidence that the BNS or NSBH models are
preferred, consistent with previous observations (Abbott
et al. 2021a). This is expected given the moderate S/N
with which GW230529 was detected (Huang et al. 2021).
The analysis of GW230529 indicates that it is an
asymmetric compact binary with a mass ratio q =
m2/m1 = 0.39+0.41
−0.12 and source component masses m1 =
3.6+0.8
−1.2 M⊙ and m2 = 1.4+0.6
−0.2 M⊙. The primary is
consistent with a black hole that resides in the lower
mass gap (3 M⊙ ≲ m1 ≲ 5 M⊙; Ozel et al. 2010;
Farr et al. 2011b), with a mass < 5 M⊙ at the 99%
credible level. The posterior distribution on the mass
of the secondary is peaked around ∼ 1.4 M⊙ with
an extended tail beyond 2 M⊙, such that P(m2 >
2 M⊙) = 5%. The mass of the secondary is con-
sistent with the distribution of known neutron star
masses, including Galactic pulsars (Antoniadis et al.
2016; Alsing et al. 2018; Özel & Freire 2016; Farrow
et al. 2019) and extragalactic GW observations (Landry
& Read 2021; Abbott et al. 2023b). Figure 1 shows
Figure 1. The one- and two-dimensional posterior
probability distributions for the component masses of the
source binary of GW230529 (teal). The contours in the
main panel denote the 90% credible regions with vertical
and horizontal lines in the side panels denoting the 90%
credible interval for the marginalized one-dimensional pos-
terior distributions. Also shown are the two O3 NSBH
events GW200105 162426 and GW200115 042309 (orange
and blue respectively; Abbott et al. 2021a) with FAR <
0.25 yr−1
(Abbott et al. 2023a), the two confident BNS
events GW170817 and GW190425 (pink and green respec-
tively; Abbott et al. 2017a, 2019a, 2020a, 2024b), as well as
GW190814 (red; Abbott et al. 2020c, 2024b) where the sec-
ondary component may be a black hole or a neutron star.
Lines of constant mass ratio are indicated by dotted gray
lines. The grey shaded region marks the 3–5 M⊙ range
of primary masses. The NSBH events and GW190814 use
combined posterior samples assuming a high-spin prior anal-
ogous to those presented in this work. The BNS events use
high-spin IMRPhenomPv2 NRTidal (Dietrich et al. 2019a)
samples.
the component mass posteriors of GW230529 relative
to other BNSs (GW170817 and GW190425) and NSBHs
(GW200105 162426 and GW200115 042309, henceforth
abbreviated as GW200105 and GW200115) observed by
the LVK as well as GW190814 (Abbott et al. 2017a,
2020a,c, 2021a).
To capture dominant spin effects on the GW signal,
we present constraints on the effective inspiral spin χeff ,
which is defined as a mass-weighted projection of the
spins along the unit Newtonian orbital angular momen-
tum vector L̂N (Damour 2001; Racine 2008; Ajith et al.
5
Figure 2. Selected source properties of GW230529.
The plot shows the one-dimensional (diagonal) and two-
dimensional (off-diagonal) marginal posterior distributions
for the primary mass m1, the mass ratio q, and the spin
component parallel to the orbital angular momentum χ1,z ≡
χ1 · L̂N. The shaded regions denote the posterior proba-
bility with the solid (dashed) curves marking the 50% and
90% credible regions for the posteriors determined using a
high spin (low spin) prior on the secondary of χ2 < 0.99
(χ2 < 0.05). The vertical lines in the one-dimensional
marginal posteriors mark the 90% credible intervals.
2014),
χeff =
m1
M
χ1 +
m2
M
χ2

· L̂N, (1)
where the dimensionless spin vector χi of each compo-
nent is related to the spin angular momentum Si by
χi = cSi/(Gm2
i ). If χeff is negative, it indicates that
at least one of the spin component projections must be
anti-aligned with respect to the orbital angular momen-
tum, i.e., χi,z ≡ χi · L̂N  0. We measure an effective
inspiral spin of χeff = −0.10+0.12
−0.17, which is consistent
with a binary in which one of the spin components is
anti-aligned or a binary with negligible spins. The mea-
surement is primarily driven by the spin component of
the primary compact object χ1,z = −0.11+0.19
−0.35, with a
probability that χ1,z  0 of 83%. However, there is a
degeneracy between the measured masses and spins of
the binary components such that more comparable mass
ratios correlate to more negative values of χeff (Cutler 
Flanagan 1994) for this system. We show the correlation
between χ1,z and the mass ratio and primary mass in
Figure 2, with more negative values of χ1,z correspond-
ing to more symmetric mass ratios and smaller primary
masses. The secondary spin is only weakly constrained
and broadly symmetric about 0, χ2,z = −0.03+0.43
−0.52. We
find no evidence for precession, with the posteriors on
the effective precessing spin χp (Schmidt et al. 2015)
being uninformative.
The presence of a neutron star in a compact binary im-
prints tidal effects onto the emitted GW signal (Flana-
gan  Hinderer 2008). The strength of this interaction is
governed by the tidal deformability of the neutron star,
which quantifies how easily the star will be deformed in
the presence of an external tidal field. In contrast, the
tidal deformability of a black hole is zero (Binnington
 Poisson 2009; Damour  Nagar 2009; Chia 2021), of-
fering a potential avenue for distinguishing between a
black hole and a neutron star. We investigate the tidal
constraints for both the primary and secondary com-
ponents using waveform models that account for tidal
effects (Dietrich et al. 2019a; Matas et al. 2020; Thomp-
son et al. 2020a), which do not qualitatively change the
mass and spin conclusions discussed above. Irrespec-
tive of whether we analyze GW230529 with a NSBH
model that assumes only the tidal deformability of the
primary compact object to be zero or a BNS model that
includes the tidal deformability of both objects, we find
the tidal deformability of the secondary object to be
unconstrained. The dimensionless tidal deformability of
the primary peaks at zero, consistent with a black hole.
The constraints on this parameter are also consistent
with dense matter equation of state (EoS) predictions
for neutron stars in this mass range.
We also perform parametrized tests of the GW phase
evolution to verify whether GW230529 is consistent with
general relativity and find no evidence of inconsisten-
cies. More detailed information on tidal deformability
analyses and testing general relativity can be found in
Appendix E.3 and Appendix F, respectively.
5. IMPACT OF GW230529 ON MERGER RATES 
POPULATIONS
We provide a provisional update to the NSBH merger
rate reported in our earlier studies (Abbott et al. 2021a,
2023b) by incorporating data from the first two weeks
of O4a using two different methods. In the first, event-
based approach, we consider GW230529 to be represen-
tative of a new class of CBCs and assume its contribu-
tion to the total number of NSBH detections to be a sin-
gle Poisson-distributed count (Kim et al. 2003; Abbott
et al. 2021a) over the span of time from the beginning of
the first observing run (O1) through the first two weeks
of O4a. We find the rate of GW230529-like mergers to
be R230529 = 55+127
−47 Gpc−3
yr−1
. When computing the
6
Figure 3. Posterior on the merger rates of NSBH systems.
The solid and dashed lines represent the broad population-
based rate calculation and the event-based rate calculation,
respectively.
rates of the significant NSBH events in O3 detected with
FAR 0.25 yr−1
(Abbott et al. 2021a, 2023a) using the
same method, we find a total event-based NSBH merger
rate of RNSBH = 85+116
−57 Gpc−3
yr−1
. Using this selec-
tion criterion, the same as Abbott et al. (2023b), the
population of NSBH mergers includes GW200105 and
GW200115; we do not include GW190814, as its source
binary is most probably a BBH (Abbott et al. 2020c;
Essick  Landry 2020; Abbott et al. 2023b).
For the second, broad population-based approach, we
consider GW200105, GW200115, and GW230529 to be
members of a single CBC class, together with an ensem-
ble of less significant candidates. The definition of this
class is determined by a simple cut on masses and spins
resulting in a NSBH-like region of parameter space. We
aggregate data from all the triggers found by GstLAL
from the beginning of O1 through the first two weeks of
O4a, assess their impact on the estimated merger rates
of NSBHs while also accounting for the possibility that
some of them are of terrestrial origin (Farr et al. 2015;
Kapadia et al. 2020), and update the NSBH merger
rate obtained at the end of O3 (Abbott et al. 2023a) to
RNSBH = 94+109
−64 Gpc−3
yr−1
. Further details regarding
the classification of triggers in the population-based rate
method can be found in Appendix G.
We show updates to both the event-based and
population-based NSBH rate constraints in Fig-
ure 3. The event-based rate estimates highlight that
GW230529-like systems merge at a similar (or poten-
tially higher) rate to the more asymmetric NSBHs iden-
tified in GWTC-3. The population-based rate estimate
is more representative of the full NSBH merger rate as
it includes less significant GW events in the data. Both
of our updated estimates are consistent with the find-
ings of Abbott et al. (2021a) within the measurement
uncertainties. Further details about rate estimates can
be found in Appendix G.
In addition to updates to the overall merger rate of
NSBHs, we also study the impact of GW230529 on the
mass and spin distributions of the compact binary pop-
ulation as inferred from GWTC-3 (Abbott et al. 2023b).
We employ hierarchical Bayesian inference to marginal-
ize over the properties of individual events and infer the
parameters of a given population model (e.g., Thrane 
Talbot 2019; Mandel et al. 2019; Vitale et al. 2020). The
updates to population model results in this work are pro-
visional because they only include one GW signal from
O4a, although the biases resulting from this selection
will not be severe since GW230529 occurred near the
start of the observing run. We quantify this by compar-
ing the event-based rate estimate (which accounts for
O4a sensitivity to compute its detectable time–volume)
with the NSBH rates attained by the various population
analyses considered in this work, finding that they are
consistent with each other.
We use three different population models in our anal-
ysis. The first two models consider the population of
compact-object binaries as a whole without distinguish-
ing by source classification, using either the parameter-
ized Power law + Dip + Break model (Fishbach
et al. 2020; Farah et al. 2022; Abbott et al. 2023b)
or the non-parametric Binned Gaussian Process
model (Mohite 2022; Ray et al. 2023b; Abbott et al.
2023b). The Power law + Dip + Break model is
designed to search for a separation in masses between
neutron stars and black holes by explicitly allowing for
a dip in the component mass distribution. The Binned
Gaussian Process model is designed to capture the
structure of the mass distribution with minimal assump-
tions about the population. The broad CBC population
analyses include all candidates reported in GWTC-3
with FAR  0.25 yr−1
, the same selection criterion used
in Abbott et al. 2023b (see Table 1 therein). The third
model we investigate (NSBH-pop; Biscoveanu et al.
2022) considers only the population of NSBH mergers
with FAR  0.25 yr−1
. NSBH-pop is a parametric
model designed to constrain the population distributions
of NSBH masses and black hole spin magnitudes. This
model assumes all analyzed events have a black hole
primary and neutron star secondary; we do not include
GW190814 in this analysis. Further details regarding
the population model parameterizations and priors can
be found in Appendix H.
7
Figure 4. The differential merger rate of NSBH systems as a function of black hole masses (solid curves: mean; shaded regions:
90% credible interval) and minimum black hole mass (dashed lines: 90% credible interval) using the NSBH-pop model with
(teal) and without (grey) GW230529. The minimum black hole mass mBH,min is a parameter of the NSBH-pop population
model, see Table 7. While the median rate is always inside the credible region, the mean can be outside the credible region.
The inclusion of GW230529 in our population analyses
has several effects on the inferred properties of NSBH
systems and the CBC population as a whole.
The inferred minimum mass of black holes in
the NSBH population decreases with the inclusion of
GW230529. The mass spectrum of black holes in the
NSBH population with and without GW230529 inferred
using the NSBH-pop model is shown in Figure 4. As
the source of GW230529 is the NSBH with the small-
est black hole mass observed to date, the minimum
mass of black holes in NSBH mergers shows a sig-
nificant decrease with the inclusion of this candidate:
mmin,BH = 3.4+1.0
−1.2 M⊙ with GW230529 compared to
mmin,BH = 6.0+1.8
−3.2 M⊙ without. In contrast, the pa-
rameter that governs the lower edge of the dip feature
in the Power law + Dip + Break model, which rep-
resents the minimum black hole mass in the CBC pop-
ulation, does not shift significantly with the inclusion
of GW230529. This difference is because the Power
law + Dip + Break model makes no assumptions
about the classification of the components and there-
fore does not enforce sharp features at the edges of each
sub-population, meaning that the source of GW230529
is not necessarily a NSBH in this model. However, the
Binned Gaussian Process and Power law + Dip
+ Break models are designed to capture the structure
of the full compact binary mass spectrum; because they
do not assign a source classification to either of the bi-
nary components, features present in these population
models can have differing astrophysical interpretations
from the NSBH-pop model.
GW230529 increases the inferred rate of compact bi-
nary mergers with a component in the 3–5 M⊙ range. A
region of interest in the mass distribution is the border
between the masses of neutron stars and black holes. We
choose ∼ 3–5 M⊙ to represent the nominal gap between
these populations. In Figure 5 we show the posterior on
the rate of mergers with one or both component masses
in the 3–5 M⊙ range, with and without GW230529.
For the Power law + Dip + Break model there
is a small increase in the merger rate within this mass
range, Rgap = 24+28
−16 Gpc−3
yr−1
with GW230529 ver-
sus Rgap = 17+25
−14 Gpc−3
yr−1
without. For the Binned
Gaussian Process model there is a larger increase
in the merger rate, Rgap = 33+89
−29 Gpc−3
yr−1
with
GW230529 versus Rgap = 7.5+46.4
−6.5 Gpc−3
yr−1
without.
The differing degree of change between the two models
is due to different assumptions for the mass ratio distri-
bution of merging compact binaries as well as the po-
tential dip in the merger rate at low black hole masses
built into the Power law + Dip + Break model.
Binned Gaussian Process does not fit for a specific
pairing function, while Power law + Dip + Break
assumes the same mass ratio distribution throughout
the whole population of CBCs. As most observed BBHs
favor equal masses, any population model conditioned
on those observations should also favor equal masses in
the BBH mass range. The implicit assumptions within
the Power law + Dip + Break model require this
preference to be imposed for all masses, including rela-
tively low-mass systems like GW230529. However, the
assumptions in Binned Gaussian Process do not
broadcast this preference as strongly across different
8
Figure 5. Posterior on the merger rate of binaries with one
or both components between 3–5 M⊙. The solid curves show
the results from the Binned Gaussian Process analysis
and the dashed curves show the results from the Power
law + Dip + Break analysis. Both models analyze the
full black hole and neutron star mass distribution. The teal
and grey curves show the analysis results with and without
GW230529, respectively.
mass scales and therefore may support more asymmet-
ric mass ratios at lower masses. Regardless of the mass
ratio distribution assumptions made by each model, we
find that the inclusion of GW230529 provides further
evidence that the ∼ 3–5 M⊙ region is not completely
empty.
GW230529 is consistent with the population inferred
from previously observed CBCs candidates. In Figure 6,
we show the population distributions of the full black
hole and neutron star mass spectrum for the primary
component of compact binary mergers using the Binned
Gaussian Process (top panel) and Power law +
Dip + Break (bottom panel) population models. We
qualitatively see that GW230529 is not an outlier with
respect to the masses of previously-observed compact
object binaries because the inclusion of GW230529 in
the population does not significantly alter the full-
population posterior constraints. This differs from the
detection of GW190814, which was an outlier with re-
spect to the rest of the observed BBH population at the
time due to its small secondary mass (Essick et al. 2022).
The observation of GW190814 strongly suggested the re-
gion between the masses of neutron stars and black holes
was populated (Abbott et al. 2023b), a conclusion that
is strengthened with the detection of GW230529 (even
though it is not an outlier).
The component masses inferred for GW230529 differ
across differing population-informed priors. In Figure 7,
Figure 6. The differential binary merger rate as a function
of the mass of the primary component using the Binned
Gaussian Process model (top panel) and the Power law
+ Dip + Break model (bottom panel) for the full compact
binary population (solid curves: mean; shaded regions: 90%
credible interval) with (teal) and without (grey) GW230529.
we show the mass and spin posteriors obtained using
priors informed by each of the population models con-
sidered in this work. The priors informed by the NSBH-
pop model prefer unequal mass ratios and small black
hole spins; they suppress the extended posterior tail out
to equal masses and anti-aligned spins. The Binned
Gaussian Process model also pulls the posteriors to
more asymmetric mass ratios and has less support for
anti-aligned spins. As shown in the top panel of Fig-
ure 6, the merger rate density inferred using the Binned
Gaussian Process model is nearly flat across the re-
gion of parameter space covered by GW230529, mean-
ing that the priors informed by this population model
have less of an impact on the shape of the posterior
compared to the parameterized models considered. Un-
like the NSBH-pop model, the Power law + Dip +
Break model has a sharp drop in the merger rate above
9
Figure 7. Posterior distributions of GW230529 under vari-
ous prior assumptions. The solid teal curve shows the poste-
rior distributions using the default high-spin priors described
in Appendix D. The various dashed and dotted curves show
posteriors obtained using population priors based on the
NSBH-pop model (orange), Binned Gaussian Process
(blue) and Power law + Dip + Break (red) models.
3 M⊙. This sharp feature results in the posterior on the
primary component being pulled below 3 M⊙ as well as
the posterior on the secondary being pulled to higher
masses. The Binned Gaussian Process model has a
similar feature, although it is closer to 2 M⊙ and there-
fore too low to significantly affect the mass estimates for
this system. The Power law + Dip + Break model
also assumes the same preference for equal-mass systems
across the entire mass spectrum, and thus, given that
the majority of the CBC population is consistent with
symmetric mass ratios, infers that the GW230529 binary
components are more similar in mass. The combination
of the drop in the differential merger rate and the pref-
erence for symmetric mass ratios increases the support
for more extreme spins oriented in the hemisphere oppo-
site the orbital angular momentum. From these models
we find that the binary source of GW230529 either has
asymmetric components with low values of χeff , or has
components that are similar in mass with χeff ∼ −0.3.
These results highlight that the choice of prior has a sig-
nificant impact on the inferred masses and spins of the
GW230529 source, and hence the inferred nature of the
binary components. We assess the nature of the compo-
nents further in Section 6. More details on the popula-
tion prior reweighting are given in Appendix H.4.
6. NATURE OF THE COMPACT OBJECTS IN
THE GW230529 BINARY
Without clear evidence for or against tidal effects in
the signal, the physical nature of the compact objects in
the GW230529 source binary can be assessed by com-
paring the measured masses and spins of each compo-
nent with the maximum masses and spins of neutron
stars allowed by previous observational data. However,
statistical uncertainties in component masses make it
especially difficult to determine whether compact ob-
jects with masses between ∼ 2.5–5 M⊙ are consistent
with being black holes or neutron stars (Hannam et al.
2013; Littenberg et al. 2015). Nevertheless, we assess
the nature of the source components by marginaliz-
ing over our uncertainties in the masses and spins of
GW230529, in the population of merging binaries, and
in the supranuclear EoS, to compute the posterior prob-
ability that each component had a mass and spin less
than the maximum mass and spin supported by the
EoS. We follow the procedure introduced in the context
of GW190814 (Abbott et al. 2020c; Essick  Landry
2020), which relied on only the maximum neutron star
mass, and has subsequently been extended to include
the effects of spin (Abbott et al. 2020c, 2021a, 2023b).
Our analysis provides only an upper limit on the prob-
ability that an object is a neutron star, as it assumes
that all objects consistent with the maximum mass and
spin of a neutron star are indeed neutron stars (Essick
 Landry 2020).
To assess the nature of the component masses of
the GW230529 source, we consider two versions of an
astrophysically-agnostic population model that is uni-
form in source-frame component masses and spin mag-
nitudes and isotropic in spin orientations: one with com-
ponent spin magnitudes χi ≡ |χi| that are allowed to be
large (χ1, χ2 ≤ 0.99) and one where they are restricted a
priori to be small (χ1, χ2 ≤ 0.05). We also consider the
Power law + Dip + Break population model (see
Appendix H.2) fit to the GW candidates from GWTC-
3 (Abbott et al. 2023a); including GW230529 in the
population model does not significantly affect the re-
sults. For each population, we marginalize over the un-
certainty in the maximum neutron star mass conditioned
on the existence of massive pulsars and previous GW ob-
servations (Landry et al. 2020) using a flexible Gaussian
process (GP) representation of the EoS (Landry  Es-
sick 2019; Essick et al. 2020b). More information on the
EoS choices can be found in Appendix I.
Table 3 reports the probability that each component
of the merger is consistent with a neutron star. In gen-
eral, we find that the secondary is almost certainly con-
sistent with a neutron star, and the primary is most
10
Table 3. Probabilistic source classification based on consistency of component masses with the maximum neutron star mass
and spin. All estimates marginalize over uncertainty in the masses, spins, and redshift of the source as well as uncertainty in the
astrophysical population and the EoS. We consider three population models: two distributions that use astrophysically-agnostic
priors and consider either large spins (χ1, χ2 ≤ 0.99) or small spins (χ1, χ2 ≤ 0.05), and a population prior using the Power
law + Dip + Break model fit with only the events from GWTC-3 (Abbott et al. 2023b). We use an EoS posterior conditioned
on massive pulsars and GW observations (Landry et al. 2020). All errors approximate 90% uncertainty from the finite number
of Monte Carlo samples used with the exception of the low-spin results for which we only place an upper or lower bound.
χ1, χ2 ≤ 0.99 χ1, χ2 ≤ 0.05 Power law + Dip + Break
P(m1 is NS) (2.9 ± 0.4)%  0.1% (8.8 ± 2.8)%
P(m2 is NS) (96.1 ± 0.4)%  99.9% (98.4 ± 1.3)%
probably a black hole. However, when incorporating
information from the Power law + Dip + Break
population model, we find that there is a ∼ 1 in 10
chance that the primary is consistent with a neutron
star. If we further relax the fixed spin assumptions im-
plicit within the Power law + Dip + Break model
for objects with masses ≤ 2.5 M⊙ from χi ≤ 0.4 to
χi ≤ 0.99 (see Appendix H.2), we can find probabilities
as high as P(m1 is NS) = (27.3 ± 3.8)%. This ambigu-
ity is similar to the secondary component of GW190814
(2.50 ≤ m2/M⊙ ≤ 2.67), which is consistent with a neu-
tron star if it was rapidly spinning (e.g., Essick  Landry
2020; Abbott et al. 2020c; Most et al. 2020a).
The differences observed between population models
primarily reflect the uncertainty in the mass ratio and
spins of the GW230529 source. For example, incorporat-
ing the Power law + Dip + Break population model
as a prior updates the posterior for m1 from 3.6+0.8
−1.2 M⊙
to 2.7+0.9
−0.4 M⊙. Additional observations of compact ob-
jects in or near the lower mass gap may clarify the com-
position of GW230529 by further constraining the ex-
act shape of the distribution of compact objects below
∼ 5 M⊙ or the supranuclear EoS.
7. IMPLICATIONS FOR MULTIMESSENGER
ASTROPHYSICS
In NSBH mergers, the neutron star can either plunge
directly into the black hole or be tidally disrupted by its
gravitational field. Tidal disruption would leave some
remnant baryonic material outside the black hole that
could potentially power a range of EM counterparts in-
cluding a kilonova (Lattimer  Schramm 1974; Li 
Paczynski 1998; Tanaka  Hotokezaka 2013; Tanaka
et al. 2014; Fernández et al. 2017; Kawaguchi et al. 2016)
or a gamma-ray burst (Mochkovitch et al. 1993; Janka
et al. 1999; Paschalidis et al. 2015; Shapiro 2017; Ruiz
et al. 2018). The conditions for tidal disruption are de-
termined by the mass ratio of the binary, the compo-
nent of the black hole spin aligned with the orbital an-
gular momentum, and the compactness of the neutron
star (Pannarale et al. 2011; Foucart 2012; Foucart et al.
2018; Krüger  Foucart 2020). While the disruption
probability of the neutron star in GW230529 can be in-
ferred based on the binary parameters, we are unlikely
to directly observe the disruption in the GW signal with-
out next-generation observatories (Clarke et al. 2023).
We use the ensemble of fitting formulae collected in
Biscoveanu et al. (2022) including the spin-dependent
properties of neutron stars (Foucart et al. 2018; Cipol-
letta et al. 2015; Breu  Rezzolla 2016; Most et al.
2020b) to constrain the remnant baryon mass outside
the final black hole following GW230529, assuming it
was produced by a NSBH merger. We additionally
marginalize over the uncertainty in the GP-EoS re-
sults obtained using the method introduced in Sec-
tion 6 (Legred et al. 2021, 2022). Using the high-spin
combined posterior samples obtained with default pri-
ors, we find a probability of neutron star tidal disruption
of 0.1, corresponding to an upper limit on the remnant
baryon mass produced in the merger of 0.052 M⊙ at 99%
credibility. The low-secondary-spin priors (χ2  0.05)
yield a tidal disruption probability and remnant baryon
mass upper limit of 0.042 and 0.011 M⊙, respectively.
A rapidly spinning neutron star is less compact than a
slowly spinning neutron star of the same gravitational
mass under the same EoS. This decrease in compactness
leads to a larger disruption probability and a larger rem-
nant baryon mass following the merger, explaining the
trend we see when comparing the results obtained un-
der the low-secondary- and high-spin priors. The source
binary of GW230529 is the most probable of the con-
fident NSBHs reported by the LVK to have undergone
tidal disruption because of the increased symmetry in its
component masses. However, the exact value of the tidal
disruption probability and the remnant baryon mass for
this system are prior-dependent.
11
Figure 8. Posterior on the fraction of NSBH systems de-
tected with GWs that may be EM bright, fEM-bright, de-
pending on the threshold remnant mass required to power
a counterpart, f(Mb
rem  Mb
rem,min). The solid and dashed
curves represent different values of the minimum remnant
mass Mb
rem,min. The teal and grey curves show the analysis
results with and without GW230529, respectively.
We can also gauge how the inclusion of GW230529
impacts estimates of the fraction of NSBH systems de-
tected in GWs that may be accompanied by an EM
counterpart, fEM-bright. Using the mass and spin dis-
tributions inferred under the NSBH-pop population
model described in Section 5, we find a 90% credi-
ble upper limit on the fraction of NSBH mergers that
may be EM-bright of fEM-bright ≤ 0.18 when includ-
ing GW230529, an increase relative to fEM-bright ≤ 0.06
obtained when excluding GW230529 from the analysis.
These estimates assume that any remnant baryon mass
Mb
rem,min ≥ 0 could power a counterpart, although the
actual threshold value is astrophysically uncertain. Fig-
ure 8 shows the posterior for fEM–bright with and with-
out the inclusion of GW230529. While the exact value
of fEM-bright depends on the assumed population model,
the increase in fEM-bright for NSBHs upon the inclusion
of GW230529 in the population is robust against mod-
eling assumptions.
Using these updated multimessenger prospects, we
can infer the contribution of NSBH mergers to the pro-
duction of heavy elements (Biscoveanu et al. 2022) and
the generation of gamma-ray bursts (Biscoveanu et al.
2023). Assuming that all remnant baryon mass pro-
duced in NSBH mergers is enriched in heavy elements
via r-process nucleosynthesis (Lattimer  Schramm
1974, 1976), we infer that NSBH mergers contribute at
most 1.1 M⊙ Gpc−3
yr−1
to the production of heavy
elements and that the rate of gamma-ray bursts with
NSBH progenitors is at most 23 Gpc−3
yr−1
at 90%
credibility. This likely represents a small fraction of
all short gamma-ray bursts, for which astrophysical
beaming-corrected rate estimates range from O(10 −
1000) Gpc−3
yr−1
(Mandel  Broekgaarden 2022), and
of the total r-process material produced by compact-
object mergers (Côté et al. 2018; Chen et al. 2021b).
No significant counterpart candidates have been re-
ported for GW230529 (IceCube Collaboration 2023;
Karambelkar et al. 2023; Lipunov et al. 2023; Longo
et al. 2023; Lesage et al. 2023; Savchenko et al. 2023;
Sugita et al. 2023a,b; Waratkar et al. 2023). This is un-
surprising given that it was only observed by a single
detector and hence was poorly localized on the sky.
8. ASTROPHYSICAL IMPLICATIONS
Since the late 1990s, there have been claims about the
existence of a mass gap between the maximum neutron
star mass and the minimum black hole mass (∼ 3–5 M⊙)
based on dynamical mass measurements of Galactic X-
ray binaries (Bailyn et al. 1998; Ozel et al. 2010; Farr
et al. 2011b). The lower edge of this purported mass
gap depends on the maximum possible mass with which
a neutron star can form in a supernova explosion, which
cannot exceed the maximum allowed neutron star mass
given by the EoS. Some EoSs support masses up to
∼ 3 M⊙ for nonrotating neutron stars (Mueller  Serot
1996; Godzieba et al. 2021) and even larger masses for
rotating neutron stars (Friedman  Ipser 1987; Cook
et al. 1994), although such large values are disfavored by
the tidal deformability inferred for GW170817 (Abbott
et al. 2019b) and Galactic observations (Alsing et al.
2018; Farr  Chatziioannou 2020). The upper edge and
extent of the mass gap depend on the minimum black
hole mass that can form from stellar core collapse. How-
ever, it remains an open question whether observational
or evolutionary selection effects inherent to the detec-
tion of Galactic X-ray binaries can lead to the observed
gap in compact object masses (Fryer  Kalogera 2001;
Kreidberg et al. 2012; Siegel et al. 2023).
In recent years, new EM observations have unveiled
a few candidates in the ∼ 3 M⊙ region, mostly from
non-interacting binary systems (Thompson et al. 2019;
van den Heuvel  Tauris 2020; Thompson et al. 2020b)
and radio surveys for pulsar binary systems (Barr
et al. 2024). Microlensing surveys do not support
the existence of a mass gap but cannot exclude it ei-
ther (Wyrzykowski et al. 2016; Wyrzykowski  Man-
del 2020). The LVK has already observed one compo-
nent of a merger whose mass falls between the most
massive neutron stars and least massive black holes
observed in the Galaxy: the secondary component of
12
GW190814 (2.5–2.7 M⊙ at the 90% credible level; Ab-
bott et al. 2020c, 2024b). The secondary components
of the GW200210 092254 and GW190917 114630 source
binaries also have support in the lower mass gap (Ab-
bott et al. 2024b, 2023a), although their mass estimates
are also consistent with a high-mass neutron star. Un-
like GW230529, the primary components of all three
of these binaries can be confidently identified as black
holes. Overall, the existence of a mass gap between the
most massive neutron stars and least massive black holes
still stands as an open question in astrophysics.
GW230529 is the first compact binary with a primary
component that has a high probability of residing in the
lower mass gap. Hence, GW230529 reinforces the con-
clusion that the 3–5 M⊙ range is not completely empty
(see Figure 5 in Section 5). However, the 3–5 M⊙ range
may still be less populated than the surrounding regions
of the mass spectrum. This conclusion is consistent with
previous population analyses and rate estimates based
on GWTC-3 (Abbott et al. 2023b).
The formation of GW230529 raises a number of ques-
tions. Given our current understanding of core collapse
in massive stars (O’Connor  Ott 2011; Janka 2012;
Ertl et al. 2020), it is unlikely that the primary compo-
nent formed via direct collapse because of its low mass,
although stochasticity in the physical mechanisms that
determine remnant mass may populate the low-mass end
of the black hole mass spectrum (Mandel  Müller 2020;
Antoniadis et al. 2022). Formation by fallback is a vi-
able scenario: recent numerical models of core-collapse
supernovae suggest that the formation of 3–6 M⊙ black
holes via substantial fallback is rare but still possible
(e.g., Sukhbold et al. 2016; Ertl et al. 2020). One-
dimensional hydrodynamical simulations of core collapse
adopting pure helium star models predict that there is
no empty gap, only a less populated region between
3–5 M⊙, with the lowest mass of black holes produced
by prompt implosions starting at ≈ 6 M⊙ (Ertl et al.
2020). Another relevant parameter is the timescale for
instability growth and launch of the core-collapse su-
pernova; if this is long enough (≳ 200 ms), the proto-
neutron star might accrete enough mass before the ex-
plosion to become a mass-gap object (Fryer  Kalogera
2001; Fryer et al. 2012). Compact binary population
synthesis models that allow for longer instability growth
timescales naturally produce merging NSBH systems
with the primary component in the lower mass gap (Bel-
czynski et al. 2012; Chattopadhyay et al. 2021; Zevin
et al. 2020; Broekgaarden et al. 2021; Olejak et al. 2022).
It may also be possible to form mass-gap objects through
accretion onto a neutron star. If the first-born neu-
tron star in the binary accretes enough material prior
to the formation of the second-born compact object, it
can trigger an accretion-induced collapse into a black
hole, yielding a mass-gap object (Siegel et al. 2023).
This scenario may be aided by super-Eddington accre-
tion onto the first-born neutron star, which has been
proposed to explain NSBHs with mass-gap black holes
like the source of GW230529 (Zhu et al. 2023). Consid-
ering the large number of uncertainties about the out-
come of core-collapse supernovae (e.g., Burrows  Var-
tanyan 2021), the primary mass of GW230529 provides a
piece of evidence to inform and constrain future models.
Overall, astrophysical models in the past have preferen-
tially adopted prescriptions that enforce the presence of
a lower-mass gap (e.g., Fryer et al. 2012), and the in-
ferred rate of GW230529-like systems urges a change of
paradigm in such model assumptions.
Alternatively, the primary component of GW230529
might be the result of the merger of two neutron stars.
For instance, the 90% credible intervals for the remnant
mass of GW190425 and the primary mass of GW230529
overlap (Abbott et al. 2020a). This may hint at a sce-
nario where the primary component could either be the
member of a former triple or quadruple system (Fra-
gione et al. 2020; Lu et al. 2021; Vynatheya  Hamers
2022; Gayathri et al. 2023), or the result of a dynami-
cal capture in a star cluster (Clausen et al. 2013; Gupta
et al. 2020; Rastello et al. 2020; Arca Sedda 2020, 2021)
or AGN disk (Tagawa et al. 2021; Yang et al. 2020).
This scenario was proposed for the formation of a com-
pact object discovered in a binary with a pulsar in
the globular cluster NGC 1851, which is measured to
have a mass of 2.09–2.71 M⊙ at 95% confidence (Barr
et al. 2024). However, dynamically-induced BNS merg-
ers are predicted to be rare in dense stellar environments
(O(10−2
) Gpc−3
yr−1
; e.g., Ye et al. 2020). Thus, the
rate of mergers between a BNS merger remnant and a
neutron star may be at least several orders of magnitude
lower than the rate we infer for GW230529-like mergers,
making this scenario improbable.
Non-stellar-origin black hole formation scenarios such
as primordial black holes (e.g., Clesse  Garcia-Bellido
2022) remain a possibility. However, there are signifi-
cant uncertainties in the predicted mass spectrum and
merger rate of primordial black hole binaries, thus mak-
ing it difficult to attribute a primordial origin to com-
pact objects that have masses consistent with predic-
tions from massive-star core collapse. Furthermore, re-
sults from microlensing surveys indicate that primordial
black hole mergers cannot be a dominant source of GWs
in the local universe (Mroz et al. 2024).
It has also been suggested that mergers apparently in-
volving mass-gap objects could instead be gravitation-
13
ally lensed BNSs (Bianconi et al. 2023; Magare et al.
2023), with the lensing magnification making them ap-
pear heavier and closer (Wang et al. 1996; Dai et al.
2017; Hannuksela et al. 2019). This scenario is diffi-
cult to explicitly test in the absence of tidal informa-
tion (Pang et al. 2020) or EM counterparts (Bianconi
et al. 2023), but the expected relative rate of strong lens-
ing is low at current detector sensitivities (Smith et al.
2023; Magare et al. 2023; Abbott et al. 2023c).
Finally, we also find mild support for the possibility
that the primary component is a neutron star rather
than a black hole when considering the population-based
Power law + Dip + Break prior that incorporates
the potential presence of a gap at low black hole masses.
In this case, GW230529 would be the most massive neu-
tron star binary yet observed, with both components
≳ 2.0 M⊙, and have non-zero spins that are anti-aligned
with the orbital angular momentum. The effective in-
spiral spin of the BNSs in this scenario would differ
significantly from BNS sources previously observed in
GWs (Abbott et al. 2017a, 2020a) as well as those in-
ferred for Galactic BNSs if they were to merge (Zhu et al.
2018). Spins oriented in the hemisphere opposite the bi-
nary orbital angular momentum could be the result of
supernova natal kicks (Kalogera 2000; Farr et al. 2011a;
O’Shaughnessy et al. 2017; Chan et al. 2020) or spin-axis
tossing (Tauris 2022) at birth. For example, one of the
neutron stars in the binary pulsar system J0737–3039
is significantly misaligned with respect to both the spin
of its companion and the orbital angular momentum of
the binary system, which may require off-axis kicks (Farr
et al. 2011a). Alternatively, isotropically-oriented com-
ponent spins that result from random pairing in dynam-
ical environments could lead to the significant spin mis-
alignment (e.g., Rodriguez et al. 2016).
9. SUMMARY
GW230529 is a GW signal from the coalescence of a
2.5–4.5 M⊙ compact object and a compact object con-
sistent with neutron star masses. The more massive
component in the merger provides evidence that com-
pact objects in the hypothesized lower mass gap exist in
merging binaries. Based on mass estimates of the two
components in the merger and current constraints on
the supranuclear EoS, we find the most probable inter-
pretation of the GW230529 source to be a NSBH coales-
cence. In this scenario, the source binary of GW230529
is the most symmetric-mass NSBH merger yet observed,
and the primary component of the merger is the lowest-
mass primary black hole (BH) observed in GWs to
date. Because NSBHs with more symmetric masses are
more susceptible to tidal disruption, the observation of
GW230529 implies that more NSBHs than previously
inferred may produce EM counterparts. However, we
cannot rule out the contrasting scenario that the source
of GW230529 consisted of two neutron stars rather than
a neutron star and a black hole. In this case, the source
of GW230529 would be the only BNS coalescence ob-
served to have strong support for non-zero and anti-
aligned spins, as well as the highest-mass BNSs system
observed to date. Regardless of the true nature of the
GW230529 source, it is a novel addition to the grow-
ing population of CBCs observed via their GW emission
and highlights the importance of continued exploration
of the CBC parameter space in O4 and beyond.
Strain data containing the signal from the LIGO Liv-
ingston observatory is available from the Gravitational
Wave Open Science Center.1
Specifically, we release
the L1:GDS-CALIB STRAIN CLEAN AR channel, where the
textttAR designation means the strain data is analy-
sis ready; this strain channel was also released at the
end of O3. Samples from the posterior distributions
of the source parameters, hyperposterior distributions
from population analyses, and notebooks for reproduc-
ing all results and figures in this paper are available on
Zenodo (Abbott et al. 2024a). The software packages
used in our analyses are open-source.
This material is based upon work supported by NSF’s
LIGO Laboratory which is a major facility fully funded
by the National Science Foundation. The authors also
gratefully acknowledge the support of the Science and
Technology Facilities Council (STFC) of the United
Kingdom, the Max-Planck-Society (MPS), and the State
of Niedersachsen/Germany for support of the construc-
tion of Advanced LIGO and construction and opera-
tion of the GEO 600 detector. Additional support for
Advanced LIGO was provided by the Australian Re-
search Council. The authors gratefully acknowledge the
Italian Istituto Nazionale di Fisica Nucleare (INFN),
the French Centre National de la Recherche Scientifique
(CNRS) and the Netherlands Organization for Scientific
Research (NWO), for the construction and operation of
the Virgo detector and the creation and support of the
EGO consortium. The authors also gratefully acknowl-
edge research support from these agencies as well as by
the Council of Scientific and Industrial Research of In-
dia, the Department of Science and Technology, India,
the Science  Engineering Research Board (SERB), In-
dia, the Ministry of Human Resource Development, In-
dia, the Spanish Agencia Estatal de Investigación (AEI),
the Spanish Ministerio de Ciencia, Innovación y Univer-
1 https://doi.org/10.7935/6k89-7q62
14
sidades, the European Union NextGenerationEU/PRTR
(PRTR-C17.I1), the Comunitat Autonòma de les Illes
Balears through the Direcció General de Recerca, In-
novació i Transformació Digital with funds from the
Tourist Stay Tax Law ITS 2017-006, the Conselleria
d’Economia, Hisenda i Innovació, the FEDER Opera-
tional Program 2021-2027 of the Balearic Islands, the
Conselleria d’Innovació, Universitats, Ciència i Societat
Digital de la Generalitat Valenciana and the CERCA
Programme Generalitat de Catalunya, Spain, the Na-
tional Science Centre of Poland and the European Union
– European Regional Development Fund; Foundation
for Polish Science (FNP), the Polish Ministry of Science
and Higher Education, the Swiss National Science Foun-
dation (SNSF), the Russian Foundation for Basic Re-
search, the Russian Science Foundation, the European
Commission, the European Social Funds (ESF), the
European Regional Development Funds (ERDF), the
Royal Society, the Scottish Funding Council, the Scot-
tish Universities Physics Alliance, the Hungarian Scien-
tific Research Fund (OTKA), the French Lyon Institute
of Origins (LIO), the Belgian Fonds de la Recherche
Scientifique (FRS-FNRS), Actions de Recherche Con-
certées (ARC) and Fonds Wetenschappelijk Onderzoek
– Vlaanderen (FWO), Belgium, the Paris Île-de-France
Region, the National Research, Development and In-
novation Office Hungary (NKFIH), the National Re-
search Foundation of Korea, the Natural Science and
Engineering Research Council Canada, Canadian Foun-
dation for Innovation (CFI), the Brazilian Ministry of
Science, Technology, and Innovations, the International
Center for Theoretical Physics South American Insti-
tute for Fundamental Research (ICTP-SAIFR), the Re-
search Grants Council of Hong Kong, the National Nat-
ural Science Foundation of China (NSFC), the Lever-
hulme Trust, the Research Corporation, the National
Science and Technology Council (NSTC), Taiwan, the
United States Department of Energy, and the Kavli
Foundation. The authors gratefully acknowledge the
support of the NSF, STFC, INFN and CNRS for pro-
vision of computational resources. This work was sup-
ported by MEXT, JSPS Leading-edge Research Infras-
tructure Program, JSPS Grant-in-Aid for Specially Pro-
moted Research 26000005, JSPS Grant-in-Aid for Scien-
tific Research on Innovative Areas 2905: JP17H06358,
JP17H06361 and JP17H06364, JSPS Core-to-Core Pro-
gram A. Advanced Research Networks, JSPS Grant-in-
Aid for Scientific Research (S) 17H06133 and 20H05639,
JSPS Grant-in-Aid for Transformative Research Areas
(A) 20A203: JP20H05854, the joint research program
of the Institute for Cosmic Ray Research, University of
Tokyo, National Research Foundation (NRF), Comput-
ing Infrastructure Project of Global Science experimen-
tal Data hub Center (GSDC) at KISTI, Korea Astron-
omy and Space Science Institute (KASI), and Ministry
of Science and ICT (MSIT) in Korea, Academia Sinica
(AS), AS Grid Center (ASGC) and the National Science
and Technology Council (NSTC) in Taiwan under grants
including the Rising Star Program and Science Van-
guard Research Program, Advanced Technology Center
(ATC) of NAOJ, and Mechanical Engineering Center of
KEK.
Software: Calibration of the LIGO strain data
was performed with GstLAL-based calibration soft-
ware pipeline (Viets et al. 2018). Data-quality prod-
ucts and event-validation results were computed us-
ing the DMT (Zweizig, J. 2006), DQR (LIGO Sci-
entific Collaboration and Virgo Collaboration 2018),
DQSEGDB (Fisher et al. 2021), gwdetchar (Urban et al.
2021), hveto (Smith et al. 2011), iDQ (Essick et al.
2020a), Omicron (Robinet et al. 2020) and PythonVir-
goTools (Virgo Collaboration 2021) software packages
and contributing software tools. Analyses in this cata-
log relied upon software from the LVK Algorithm Li-
brary Suite (LIGO Scientific, Virgo, and KAGRA Col-
laboration 2018). The detection of the signals and sub-
sequent significance evaluations were performed with
the GstLAL-based inspiral software pipeline (Messick
et al. 2017; Sachdev et al. 2019; Hanna et al. 2020;
Cannon et al. 2021), with the MBTA pipeline (Adams
et al. 2016; Aubin et al. 2021), and with the Py-
CBC (Usman et al. 2016; Nitz et al. 2017; Davies
et al. 2020) packages. Estimates of the noise spectra and
glitch models were obtained using BayesWave (Cor-
nish  Littenberg 2015; Littenberg et al. 2016; Cor-
nish et al. 2021). Low-latency source localization was
performed using BAYESTAR (Singer  Price 2016).
Source-parameter estimation was primarily performed
with the Bilby and Parallel Bilby libraries (Ashton
et al. 2019; Smith et al. 2020; Romero-Shaw et al. 2020)
using the Dynesty nested sampling package (Spea-
gle 2020). SEOBNRv5PHM waveforms used in param-
eter estimation were generated using pySEOBNR (Mi-
haylov et al. 2023). PESummary was used to postpro-
cess and collate parameter-estimation results (Hoy 
Raymond 2021). The various stages of the parameter-
estimation analysis were managed with the Asimov li-
brary (Williams et al. 2023). Plots were prepared with
Matplotlib (Hunter 2007), seaborn (Waskom 2021)
and GWpy (Macleod et al. 2021). NumPy (Harris et al.
2020) and SciPy (Virtanen et al. 2020) were used for
analyses in the manuscript.
15
APPENDIX
A. UPGRADES TO THE DETECTOR NETWORK FOR O4
The Advanced LIGO, Advanced Virgo, and KAGRA detectors have all undergone a series of upgrades to improve
the network sensitivity in preparation for O4. In this section, we focus on upgrades made to the LIGO Livingston
observatory as it was the only detector to observe GW230529; similar upgrades were made at LIGO Hanford. Some
of these improvements are a part of the Advanced LIGO Plus (A+) detector upgrades (Abbott et al. 2020b).
The principal commissioning work done in preparation for O4 was to enhance the optics systems in the detector.
The pre-stabilized laser was redesigned for O4 with amplifiers allowing input power up to 125 W (Bode et al. 2020;
Cahillane  Mansell 2022). LIGO Livingston operated at 63 W in O4a. Both end test masses at LIGO Livingston
were replaced because their mirror coatings contained small, point-like absorbers that limited detector sensitivity by
degrading the power-recycling gain (Brooks et al. 2021). For O4, frequency-dependent squeezing was implemented
with the addition of a 300 m filter cavity to rotate the squeezed vacuum quadrature across the bandwidth of the
detector (Dwyer et al. 2022; McCuller et al. 2020). With frequency-dependent squeezing, uncertainty is reduced in
both the amplitude and phase quadratures, allowing for a broadband reduction in quantum noise (Ganapathy et al.
2023). Squeezing was implemented independently of frequency in O3, which only reduced the quantum noise at high
frequencies (Tse et al. 2019).
Other commissioning work was done to improve data quality and reduce noise at low frequencies. For O4, scattered
light noise was mitigated by removing some problematic scattering surfaces, and improving the resonant damping of
other scatterers (Soni et al. 2020; Davis et al. 2021). Low-frequency technical noise (i.e., noise that is not intrinsic to
the detector design, but can limit the detector sensitivity and performance) was reduced with the commissioning of
feedback control loops, noise subtraction, and better electronics. Overall, the upgrades made during the commissioning
period for O4 led to a broadband reduction in noise and improvement in detector sensitivity and performance.
B. DETECTION TIMELINE AND CIRCULARS
The LVK issues low-latency alerts to facilitate prompt follow-up of GW candidates (Chaudhary et al. 2023).
GW230529 was initially identified in a low-latency search using data from the LIGO Livingston observatory. The
candidate was given the name S230529ay in the Gravitational-Wave Candidate Event Database (GraceDB).2
After the detection of GW230529, an initial notice was sent out to astronomers through NASA’s General Coordinates
Network (GCN) (LIGO Scientific, Virgo, and KAGRA Collaboration 2023a). The sky localization computed in low
latency by BAYESTAR (Singer  Price 2016; Singer et al. 2016) had a 90% credible area of ≈ 24200 deg2
; the large
credible area was due to GW230529 only being observed by a single detector. The initial alert also included low-latency
estimates of the mass-based source classification (BNS, BBH, and NSBH) produced by the PyCBC pipeline (Villa-
Ortega et al. 2022). Additional estimates that the source binary of GW230529 contained at least one neutron star,
contained at least one compact object in the lower mass gap 3–5 M⊙, and had neutron-star matter ejected outside the
final compact object were produced by a machine learning method trained to infer source properties from the search
pipeline results (Chatterjee et al. 2020). The estimated probability that the source binary of GW230529 included at
least one neutron star was  99.9%.
Low-latency parameter estimation was performed with Bilby (Ashton et al. 2019; Romero-Shaw et al. 2020) and used
to produce an updated sky localization and estimates of source properties sent out in another alert (LIGO Scientific,
Virgo, and KAGRA Collaboration 2023b). The updated sky localization had a 90% credible area of ≈ 25600 deg2
.
The updated estimate of source properties led to a slight decrease in the probability that the source binary included
at least one neutron star, which was updated to 98.5%.
C. QUANTIFYING SIGNIFICANCE FOR A SINGLE-DETECTOR CANDIDATE EVENT
Each search pipeline has its own method for calculating the FAR of a single-detector GW candidate. In this section
we will summarize these methods.
2 https://gracedb.ligo.org/
16
Figure 9. The noise background for the LIGO Livingston observatory collected by the GstLAL pipeline in offline mode, with
the S/N–ξ2
values of GW230529 overlaid. The test statistic ξ2
measures signal consistency. The background is collected from
templates that are part of the same bin as the template that recovered GW230529, and is consequently the background used
to rank GW230529 and calculate its significance. The background distribution has effectively no support at the position of
GW230529. The colorbar represents the probability of producing a certain S/N and ξ2
from noise triggers.
C.1. GstLAL
The GstLAL pipeline assigns a likelihood ratio to all of its candidate signals as the ranking statistic to estimate
their significance. The likelihood ratio is the ratio of the probability of obtaining the candidate under the signal
hypothesis to the probability of obtaining the candidate under the noise hypothesis. The latter probability is largely
calculated by collecting S/N and ξ2
statistics of noise triggers during the analysis, where ξ2
is a signal consistency
test statistic (Messick et al. 2017). Similar templates in the template bank are grouped together on the basis of the
post-Newtonian (PN) expansion of their waveforms (Morisaki  Raymond 2020; Sakon et al. 2024). Each template bin
collects its own S/N and ξ2
statistics, which get used to rank candidates recovered by templates in that bin. Further
details about the calculation of the probability of obtaining the candidate under the noise hypothesis, as well as the
GstLAL likelihood ratio in general can be found in Tsukada et al. (2023). The S/N–ξ2
statistics collected from noise
triggers from the same template bin as GW230529 with GW230529 superimposed are shown in Figure 9. GW230529
clearly stands out from the background, and there are no noise triggers at its position in S/N–ξ2
space.
Since non-stationary noise transients known as glitches (Nuttall 2018) are not expected to be correlated across
detectors, single-detector GW candidates, whether during times when a single or multiple detectors are observing,
are more likely to be glitches as compared to coincident GW candidates. To account for this, the GstLAL pipeline
downweights the logarithm of the likelihood ratio of single-detector candidates by subtracting an empirically-tuned
factor of 13, which is optimized to maximize the recovery of candidates with an astrophysical origin while minimizing
the recovery of glitches (Abbott et al. 2020a). The FAR of the GstLAL pipeline for GW230529 quoted in Table 1 is
calculated after the application of this penalty.
Finally, the FAR for a candidate in the search is computed by comparing its likelihood ratio to the likelihood ratios
of noise triggers not found in coincidence, after accounting for the live-time of the analysis. These noise triggers not
found in coincidence allow the pipeline to extrapolate the background distribution of likelihood ratios to large values,
enabling the inverse FAR of a candidate to be greater than the duration of the analysis. While in the low-latency
mode, the GstLAL FAR calculation uses the background from the start of the analysis period until the time of the
candidate. In contrast, for its offline analysis, the GstLAL pipeline uses background collected from the full analysis
period including the entirety of O4a to rank candidates. This differs from the other search pipelines presented in
this work which only use background from the first two weeks of O4a for their offline search results presented here.
The GstLAL offline analysis was performed using the same template bank as the online analysis (Sakon et al. 2024;
Ewing et al. 2023). Details are liable to change for future offline GstLAL analyses in O4a. However, for such a
17
Figure 10. Ranking statistic distribution of MBTA single-detector triggers in the LIGO Livingston observatory during the
first two weeks of O4, excluding significant public alerts aside from GW230529.
significant candidate as GW230529, we do not expect these changes to impact its interpretation as highly likely being
of astrophysical origin.
C.2. MBTA
The MBTA single-detector candidate search for O4a focuses on a subset of the full MBTA parameter space. The goal
is to focus on BNS and NSBH signals, which are most interesting because of their rarity and possible EM counterparts.
Their long signal duration also makes them easier to identify and allows for a better sensitivity to be reached when
compared to a single-detector candidate search using the whole MBTA parameter space. The parameter space for the
O4a online single-detector search was defined based on the detector-frame (redshifted) primary mass and chirp mass
of the templates and motivated by the computation of the probability for whether a non-zero amount of neutron star
material remained outside the final remnant compact object (Chatterjee et al. 2020) introduced in Appendix B. The
considered space is (1 + z) m1  50 M⊙ and (1 + z) M  5 M⊙ (Juste 2023). For the offline analysis, this space was
adapted and we consider only (1 + z) M  7 M⊙. MBTA online also applied selection criteria based on data-quality
tests to its single-detector candidates (Juste 2023). This was changed to a reweighting of the ranking statistic for the
offline analysis.
The ranking statistic for MBTA single-detector triggers is a reweighted S/N. The reweighting is based on the
computation of a quantity called auto χ2
(Aubin et al. 2021), which tests the consistency of the time evolution of the
S/N time series. The additional reweighting used in the offline analysis relies on the computation of a quantity that
identifies an excess of S/N for single-detector triggers. The excess of S/N is larger for triggers that have a noise origin
compared to astrophysical signals or injections, and therefore allows for discrimination between astrophysical signals
and noise. The ranking statistic distribution of the MBTA offline analysis for single-detector triggers during the first
two weeks of O4a is shown in Figure 10. Other triggers which produced significant public alerts have been removed
from the plotted distribution. GW230529 stands out from the background with a high ranking statistic that reflects
the auto χ2
value being completely consistent with a signal origin.
The FAR in MBTA is a function of pastro (Andres et al. 2022), the probability of astrophysical origin of the
candidate. It is derived from the combined parametrizations of the FAR as a function of the ranking statistic and
of pastro as a function of the ranking statistic. Inverting the latter gives the ranking statistic as a function of pastro
and eventually the FAR as a function of pastro. The background estimation for MBTA single-detector triggers was
computed differently during the online and offline analyses. The online analysis relies on the computation of simulated
single-detector triggers obtained through random combinations of single frequency-band data (Juste 2023). O4a online
analysis and the method of randomly combining single-frequency band data showed that the background for MBTA
single-detector triggers follows an exponential distribution and is stable in time beyond statistical fluctuations. This
prompted us to update the model we use for the offline (and future) analyses to reach greater sensitivity. This new
model involves extrapolating the observed distribution of single-detector triggers and removing the significant triggers.
18
Figure 11. Ranking statistic distribution of PyCBC offline single-detector triggers in the LIGO Livingston observatory during
the first two weeks of O4. The plotted distribution may include triggers from other less-significant signals arriving during the
period analyzed.
A safety margin is used in the extrapolation such that the FAR is over-estimated relative to the best-fit extrapolated
distribution. This change in methods, in addition to the difference in handling of single-detector triggers online and
offline, explains the difference in inverse FAR for the online (1.1 yr) and offline (1000 yr) analyses.
C.3. PyCBC
In PyCBC, each GW candidate is assigned a ranking statistic, and then a FAR is calculated by comparing the
ranking statistic of the candidate to the background distribution. The details of this procedure differ between the
online and offline versions of the PyCBC search.
In the online pipeline, we consider single-detector candidates only from templates with duration greater than 7 s
above a starting frequency of 17 Hz, corresponding to a range of masses and spins for which EM emission due to
neutron star ejecta might be expected. Low-latency data quality timeseries produced by iDQ, a machine learning
framework for autonomous detection of noise artifacts using only auxiliary data channels insensitive to GWs (Essick
et al. 2020a), are used to veto candidates at times when a glitch is likely to be present in the data. The remaining
single-detector candidates are ranked by the reweighted S/N described in Nitz (2018). Only candidates with a χ2
statistic (Allen 2005)  2.0 and reweighted S/N  6.75 are kept. The rate density of single-detector triggers above
the reweighted S/N threshold is fit with a decreasing exponential.
In offline PyCBC, we only consider single-detector candidates from templates with duration greater than 0.3 s
above a starting frequency of 15 Hz. We also require that candidates have a χ2
statistic  10.0, a reweighted S/N
 5.5, and a PSD variation statistic (Mozzon et al. 2020)  10.0, in order to exclude high-amplitude noise transients.
Each candidate is assigned a ranking statistic equal to the logarithm of the ratio of astrophysical signal likelihood to
detector noise likelihood. The PyCBC O4 offline search introduced two changes to the ranking statistic relative to
the O3 calculation. First, an explicit model of the signal distribution covering the space of binary masses and spins is
included (Kumar  Dent 2024). The model is designed to maximize the number of detected signals from the known
compact binary distribution, while also maintaining sensitivity to signals in previously unpopulated regions. Second,
the model of the rate density of events caused by detector noise now includes a term describing the variation in rate
during times of heightened detector noise (Davis et al. 2022). The rate density of single-detector candidates above a
ranking statistic threshold of 0 is fit with a decreasing exponential.
In both the online and offline versions of PyCBC, the exponential fit of trigger rate density above the relevant
ranking statistic threshold is used to extrapolate the FAR of single-detector candidates beyond the observing time of
the search (Cabourn Davies  Harry 2022). The FAR calculations for GW230529 used triggers from the first two weeks
of O4 at the LIGO Livingston observatory. The distribution of ranking statistics for offline single-detector candidates
at the LIGO Livingston observatory is shown in Figure 11. Similar to the other searches, GW230529 clearly stands
out from the background distribution.
19
Table 4. Summary of parameter-estimation analysis choices for GW230529, and the physical content of each waveform model
used. Here, tides refers to modeling of neutron star tidal deformability and disruption when tidal forces overcome the self-gravity
of the neutron star. The spin prior denotes any restrictions on the spin magnitude of the binary components.
Waveform Model Precession Higher Multipoles Tides Disruption Spin Prior
IMRPhenomNSBH − − ✓ ✓ χ1  0.50, χ2  0.05
IMRPhenomPv2 NRTidalv2 ✓ − ✓ − χ1  0.99, χ2  0.05
IMRPhenomXPHM ✓ ✓ − − χ1  0.99, χ2  0.99
SEOBNRv5PHM ✓ ✓ − − χ1  0.99, χ2  0.99
SEOBNRv4 ROM NRTidalv2 NSBH − − ✓ ✓ χ1  0.90, χ2  0.05
IMRPhenomXPHM ✓ ✓ − − χ1  0.99, χ2  0.05
IMRPhenomXP ✓ − − − χ1  0.99, χ2  0.99
IMRPhenomXHM − ✓ − − χ1  0.99, χ2  0.99
IMRPhenomXAS − − − − χ1  0.99, χ2  0.99
IMRPhenomXAS − − − − χ1  0.50, χ2  0.05
IMRPhenomPv2 NRTidalv2 ✓ − ✓ − χ1  0.05, χ2  0.05
IMRPhenomXPHM ✓ ✓ − − χ1  0.05, χ2  0.05
SEOBNRv5PHM ✓ ✓ − − χ1  0.99, χ2  0.05
D. PRIORS, WAVEFORM SYSTEMATICS, AND BAYES FACTORS
Given the uncertain nature of the compact objects, we analyze GW230529 with a suite of models that incorporate a
number of key physical effects. The choices of data duration (128 s) and frequency bandwidth (20–1792 Hz) analyzed
were informed by comparing waveforms spanning the mass range recovered in preliminary analyses to the detector
noise PSD at the time of the event. The high-frequency cutoff is chosen to avoid loss of power at high frequencies due
to low-pass filtering of the data. For a subset of the signal models below, we employ a range of techniques to speed
up the evaluation of the likelihood including heterodyning (also known as relative binning; Cornish 2010; Zackay et al.
2018; Cornish 2021; Krishna et al. 2023), multibanding (Garcı́a-Quirós et al. 2021; Morisaki 2021), and reduced order
quadratures (Canizares et al. 2015; Smith et al. 2016; Morisaki et al. 2023).
The physical effects included and the spin prior ranges for each waveform model considered in this work are shown
in Table 4. All analyses use mass priors that are flat in the redshifted component masses with chirp masses, M =
(m1m2)3/5
/(m1 +m2)1/5
∈ [2.0214, 2.0331] M⊙ and mass ratios q ∈ [0.125, 1]. The luminosity distance prior is uniform
in comoving volume and source-frame time on the range DL ∈ [1, 500] Mpc. The priors on the tidal deformability
parameters are chosen to be uniform in the component tidal deformabilities over Λ ∈ [0, 5000]. Standard priors (e.g.,
Romero-Shaw et al. 2020; Abbott et al. 2024b) are used for all the other extrinsic binary parameters. Below we provide
further motivation for considering this suite of waveform models.
The primary analysis in this work uses the IMRPhenomXPHM and SEOBNRv5PHM BBH waveform models (corre-
sponding to the third and fourth rows in Table 4), which provide an accurate description of BBHs but do not incorporate
tidal effects or the potential tidal disruption of a companion neutron star. We did not consider an extension of IMR-
PhenomXPHM that incorporates additional physics beyond the two precessing higher-order multipole moment BBH
models used here as these effects only enter at high frequencies and are not relevant for this event (Thompson et al.
2024). In order to quantify the impact of neglecting tidal physics, we analyze GW230529 with NSBH and BNS wave-
form models that incorporate different tidal information. The NSBH models only incorporate tidal information from
the less massive compact object, are restricted to spins aligned with the orbital angular momentum, and only model
20
the dominant ℓ = m = 2 multipole moment. However, they do model the possible tidal disruption of the neutron star,
which occurs when tidal forces of the black hole dominate over the self-gravity of the neutron star.
We use two NSBH models, a frequency-domain phenomenological model IMRPhenomNSBH (Thompson et al. 2020a),
and a frequency-domain effective-one-body surrogate model SEOBNRv4 ROM NRTidalv2 NSBH (Matas et al. 2020).
IMRPhenomNSBH uses the BBH models IMRPhenomC (Santamaria et al. 2010) and IMRPhenomD (Husa et al. 2016;
Khan et al. 2016) as baselines for the amplitude and phase, respectively, incorporating corrections to the phase due
to tidal effects following the NRTidal model (Dietrich et al. 2017, 2019b,a) and to the amplitude following Pannarale
et al. (2013, 2015). SEOBNRv4 ROM NRTidalv2 NSBH uses the SEOBNRv4 BBH model as a baseline (Bohé et al.
2017) and applies the same corrections to account for tidal deformability and disruption as IMRPhenomNSBH but
is additionally calibrated against numerical relativity (NR) simulations of NSBH mergers (Foucart et al. 2013, 2014,
2019; Kyutoku et al. 2010, 2011). As the NSBH waveform models do not capture spin-induced orbital precession,
we analyze GW230529 with the aligned-spin BBH waveform models IMRPhenomXAS (Pratten et al. 2020), which
only contains the dominant harmonic, and IMRPhenomXHM (Garcı́a-Quirós et al. 2020), which includes higher-order
multipole moments. Models for NSBH binaries that contain both higher-order multipole moments and precession are
under active development (Gonzalez et al. 2023) and could potentially allow for a more consistent model selection
between the different source categories.
Given that the mass of the primary overlaps with current estimates of the maximum known neutron star mass (Landry
 Read 2021; Romani et al. 2022), we also analyze GW230529 with a BNS waveform model that allows for tidal interac-
tions on both the primary and the secondary components of the binary. We use IMRPhenomPv2 NRTidalv2 (Dietrich
et al. 2019a), which adds a model for the tidal phase that is calibrated against both effective-one-body (EOB) and NR
simulations to the underlying precessing-spin point-particle waveform model IMRPhenomPv2 (Hannam et al. 2014).
A limitation is that IMRPhenomPv2 NRTidalv2 is calibrated against a suite of equal-mass, non-spinning BNS NR
simulations, where the maximum neutron star mass is only 1.372 M⊙. Nevertheless, the model has been validated
against a catalog of EOB–NR hybrid waveforms that includes asymmetric configurations and heavier neutron star
masses (Dietrich et al. 2019a; Abac et al. 2024). Because of large uncertainties in BNS postmerger waveform modeling,
IMRPhenomPv2 NRTidalv2 includes an amplitude taper from 1–1.2 times the estimated merger frequency (Dietrich
et al. 2019b). The resulting suppression of S/N at these frequencies may be responsible for the posterior differences
between IMRPhenomPv2 NRTidalv2 and the BBH and NSBH waveform models we consider (see Figure 12).
From the mass estimates alone, the secondary object is consistent with being a neutron star. As such, we follow
earlier analyses and analyze GW230529 with two spin priors (Abbott et al. 2021a): an agnostic high-spin prior and an
astrophysically motivated low-spin prior. The high-spin prior assumes that the spins on both objects are isotropically
oriented and have dimensionless spin magnitudes that are uniformly distributed up to χ1, χ2 ≤ 0.99. The low-spin
prior, on the other hand, is inspired by the extrapolated maximum spin observed in Galactic BNSs that will merge
within a Hubble time (Burgay et al. 2003; Stovall et al. 2018), and restricts the spin magnitude of the secondary to
be χ2 ≤ 0.05 while keeping χ1 ≤ 0.99. As the nature of the primary as a black hole or neutron star is uncertain, we
also use a third choice of prior where both spins are restricted to χ1, χ2 ≤ 0.05 for the IMRPhenomPv2 NRTidalv2
and IMRPhenomXPHM waveform models (rows 11 and 12 of Table 4, respectively). The purpose of using multiple
priors is to help gauge whether astrophysical assumptions on the neutron star spin impact any of the statements on
the probability that the primary object lies in the lower mass gap. In Figure 12, we show the impact of waveform
systematics and prior assumptions on the strongly correlated mass ratio–effective inspiral spin distribution.
The degree to which a given waveform model under certain assumptions matches the data can be gauged using
the Bayes factor. However, Bayes factors penalize extra degrees of freedom in models that do not improve the fit
when those extra degrees of freedom are constrained by the data (Mackay 2003). We find no significant preference
(log10 B ≲ 0.5) between the high-spin and low-spin prior on the secondary; we similarly do not find a statistical
preference for or against the effects of precession, higher-order multipole moments, or tidal deformation or disruption
of the secondary object.
E. ADDITIONAL SOURCE PROPERTIES
E.1. Component Spins and Precession
Assuming a high-spin prior, the posteriors for the primary spin magnitude are only weakly informative, disfavoring
zero and extremal spins with χ1 = 0.07–0.85. For the secondary, the posteriors are even less informative. Under
the low-spin prior, the primary spin magnitude posterior is peaked at slightly higher values with zero and extremal
21
Figure 12. The two-dimensional q–χeff posterior probability distributions for GW230529 using various BBH, NSBH, and BNS
signal models. The vertical dotted lines indicate primary masses that have been mapped to the mass ratio given the median
chirp mass estimated from the IMRPhenomXPHM high-spin analysis.
spins being disfavored to a larger degree, χ1 = 0.10–0.84. The secondary spin is completely uninformative over the
restricted range of spin magnitudes. The joint two-dimensional posterior probability distribution of the dimensionless
spin magnitude and the spin tilt are shown in Figure 13. Regions of high (low) probability are denoted by a darker
(lighter) shade.
When the spins are misaligned with the orbital angular momentum, relativistic spin-orbit and spin-spin couplings
drive the evolution of the orbital plane and the spins themselves (Apostolatos et al. 1994; Kidder 1995). The leading-
order effect can be captured by an effective precession spin parameter, 0 ≤ χp ≤ 1, which approximately measures
the degree of in-plane spin and can be used to parameterize the rate of precession of the orbital plane (Schmidt et al.
2015)
χp = max

χ1 sin θ1,

3 + 4q
4 + 3q

q χ2 sin θ2

. (E1)
We find the constraints on χp to be uninformative, and we are not able to make any significant statements on
precession. The uninformative nature of these results is corroborated by the Bayes factor between the precessing and
non-precessing phenomenological waveform models, log10 BXP
XAS = 0.22.
E.2. Source Location and Distance
As GW230529 was a single-detector observation, the sky localization is poor and covers a sky area of ≈ 24100 deg2
at the 90% credible level. The luminosity distance is inferred to be DL = 201+102
−96 Mpc, corresponding to a redshift
of z = 0.04+0.02
−0.02 computed using the Planck 2015 cosmological parameters (Ade et al. 2016). The luminosity distance
has a degeneracy with the inclination angle of the binary’s total angular momentum with respect to the line of
sight, θJN (e.g., Cutler  Flanagan 1994; Nissanke et al. 2010; Aasi et al. 2013; Vitale  Chen 2018). The posterior
distribution on θJN is broadly unconstrained, showing no preference for a total angular momentum vector that is
pointed towards or away from the line of sight.
E.3. Tidal Deformability
The tidal deformability of a neutron star is defined by
λ =
2
3
k2R5
, (E2)
22
Figure 13. Two-dimensional posterior probability distributions for the spin magnitude χi and the spin-tilt angle θi for the
primary (left) and secondary (right) compact objects at a reference frequency of 20 Hz. A spin-tilt angle of 0◦
(180◦
) indicates
a spin that is perfectly aligned (anti-aligned) with the orbital angular momentum L̂. The pixels have equal prior probability,
and shading denotes the posterior probability of each pixel of the high-spin prior analysis, after marginalizing over azimuthal
angles. The solid (dashed) contours denote the 90% credible region for the high-spin (low-spin) prior analyses respectively. The
probability distributions are marginalized over the azimuthal spin angles.
where k2 is the gravitational Love number of the object and R is its radius (Damour et al. 1992; Mora  Will 2004;
Flanagan  Hinderer 2008; Damour  Nagar 2009). However, it is often convenient to introduce a dimensionless tidal
deformability
Λ =
λ
m5
=
2
3
k2C−5
, (E3)
where C = m/R is the compactness of the neutron star in geometrized units.
Using the IMRPhenomPv2 NRTidalv2 model, which allows for tidal deformability on both objects but does not
model tidal disruption, we infer Λ1 ≤ 1462 at 90% credibility with the χ1  0.99, χ2  0.05 spin prior; the posterior
peaks at Λ1 = 0. We do not constrain Λ2 relative to the prior. Constraints on the tidal deformability Λ of both
components of GW230529 are shown in Figure 14, along with the tidal deformabilities predicted for the secondary
object under the BSK24 neutron star EoS (Goriely et al. 2013; Pearson et al. 2018; Perot et al. 2019) and using
the Gaussian process (GP)-EoS constraints introduced in Section 6. BSK24 is chosen as an illustrative EoS that is
thermodynamically consistent and falls within the range of support of constraints from nuclear physics and astrophysics,
including GW170817. The uninformative Λ2 posterior is consistent with both of these predictions. In addition to the
tidal deformability posteriors, we use two distinct likelihood interpolation schemes (Ray et al. 2023a; Landry  Essick
2019) to directly constrain the neutron star EoS using both spectral (Lindblom 2010; Lindblom  Indik 2012, 2014)
and GP (Landry  Essick 2019; Essick et al. 2020b) representations. Both methods incorporate consistency with the
observed heavy pulsars PSR J0740+6620 (Fonseca et al. 2021) and PSR J0348+0432 (Antoniadis et al. 2013) as priors
on the EoS and enforce thermodynamic stability and causality. Unlike other analyses where the GP representations
are conditioned on both GW and pulsar data, here we only include the pulsar constraints in the prior, in order to
distinguish the EoS information provided by GW230529 alone. These direct EoS inferences are also uninformative,
returning their respective priors.
23
Figure 14. Constraints on dimensionless tidal deformability Λ for the primary (green dashed) and secondary (green solid)
components of GW230529. We also show tidal deformabilities predicted for the secondary object under the BSK24 neutron
star EoS (navy; Goriely et al. 2013; Pearson et al. 2018; Perot et al. 2019) and constraints obtained from BNS and pulsar
observations using the GP model (GP-EoS; red).
F. TESTING GENERAL RELATIVITY
To verify whether GW230529 is consistent with general relativity, we perform parameterized tests searching for
deviations in the PN coefficients that determine the phase evolution of the GW signal (Blanchet  Sathyaprakash
1994, 1995; Arun et al. 2006a,b; Yunes  Pretorius 2009; Mishra et al. 2010; Li et al. 2012a,b). Specifically, we
search for parametric deviations to the GW inspiral phasing applied to the frequency-domain waveform models IM-
RPhenomXP NRTidalv2 (Colleoni et al. 2023) and IMRPhenomXPHM (Pratten et al. 2020; Garcı́a-Quirós et al.
2020; Pratten et al. 2021) using the TIGER framework (Agathos et al. 2014; Meidam et al. 2018), and SEOB-
NRv4 ROM NRTidalv2 NSBH (Matas et al. 2020) and SEOBNRv4HM ROM (Bohé et al. 2017; Cotesta et al. 2018,
2020) using the FTI framework (Mehta et al. 2023a). These waveform models each capture different physical effects
(precession, higher-order multipole moments, and neutron star tidal deformability) to determine whether their absence
in the model leads to inferred inconsistencies with general relativity.
For all waveform models and PN orders whose analyses have been completed, we find that GW230529 is consistent
with general relativity within the inferred uncertainties on the deviation parameters. We do not yet include results
about 0PN deviations, which are being examined separately due to technical issues related to the degeneracy between
the 0PN deviation parameter and the chirp mass (Payne et al. 2023). The constraints obtained at −1PN are an order
of magnitude tighter than previously reported bounds for NSBH and BBH (Abbott et al. 2021b). The previously
reported bounds using GW170817 remain the tightest constraints on −1PN deviations obtained with GWs (Abbott
et al. 2019c). Further details about the tests of general relativity performed will be presented in a follow-up paper.
G. COMPACT BINARY MERGER RATES METHODS
A key component of the event-based rate estimation described in Section 5 is the sensitive time–volume of our GW
searches. The sensitivities to GW200105-, GW200115-, and GW230529-like events are computed from O1 through the
first two weeks of O4a according to the corresponding mass and spin posteriors from the IMRPhenomXPHM high-spin
analyses of these signals. The posterior samples chosen for this analysis are consistent with previous event-based rate
estimates presented for NSBH mergers (Abbott et al. 2021a). Simulated signals, whose binary parameters are drawn
from the mass and spin posteriors for each signal, are distributed uniformly in comoving volume and following the other
extrinsic parameter distributions given in Appendix D, and are added to simulated detector noise characterized by
representative PSDs for each observing run. The detectability of these injections is then calculated semi-analytically
to determine the sensitive time–volume by calculating network responses to the simulated signals and applying a
threshold on the network optimal S/N of  10. This choice of threshold was previously tuned to the results of matched
filter searches (Abbott et al. 2021c), and is comparable to threshold statistics calculated for semi-analytic sensitivity
estimates (Essick 2023).
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star
Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star

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Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star

  • 1. Draft version April 5, 2024 Typeset using L A TEX twocolumn style in AASTeX631 Observation of Gravitational Waves from the Coalescence of a 2.5–4.5 M⊙ Compact Object and a Neutron Star The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration ABSTRACT We report the observation of a coalescing compact binary with component masses 2.5–4.5 M⊙ and 1.2–2.0 M⊙ (all measurements quoted at the 90% credible level). The gravitational-wave sig- nal GW230529 181500 was observed during the fourth observing run of the LIGO–Virgo–KAGRA detector network on 2023 May 29 by the LIGO Livingston observatory. The primary component of the source has a mass less than 5 M⊙ at 99% credibility. We cannot definitively determine from gravitational-wave data alone whether either component of the source is a neutron star or a black hole. However, given existing estimates of the maximum neutron star mass, we find the most probable interpretation of the source to be the coalescence of a neutron star with a black hole that has a mass between the most massive neutron stars and the least massive black holes observed in the Galaxy. We estimate a merger rate density of 55+127 −47 Gpc−3 yr−1 for compact binary coalescences with properties similar to the source of GW230529 181500; assuming that the source is a neutron star–black hole merger, GW230529 181500-like sources constitute about 60% of the total merger rate inferred for neu- tron star–black hole coalescences. The discovery of this system implies an increase in the expected rate of neutron star–black hole mergers with electromagnetic counterparts and provides further evidence for compact objects existing within the purported lower mass gap. Keywords: Gravitational wave astronomy(675) — Gravitational wave detectors(676) — Gravitational wave sources(677) — Stellar mass black holes(1611) — Neutron stars(1108) 1. INTRODUCTION In May 2023, the fourth observing run (O4) of the Ad- vanced LIGO (Aasi et al. 2015), Advanced Virgo (Acer- nese et al. 2015), and KAGRA (Somiya 2012; Aso et al. 2013) observatory network commenced following a series of upgrades to increase the sensitivity of the network. The prior three observing runs opened the field of ob- servational gravitational-wave (GW) astronomy, with 90 probable compact binary coalescence (CBC) candidates reported by the LIGO Scientific, Virgo, and KAGRA Collaboration (LVK) at the conclusion of the third ob- serving run (O3) (Abbott et al. 2023a) and further can- didates found by external analyses (e.g., Nitz et al. 2023; Mehta et al. 2023b; Wadekar et al. 2023). These in- cluded the first observation of merging stellar-mass black holes (Abbott et al. 2016a), the first observation of a stellar-mass black hole merging with a neutron star (Ab- bott et al. 2021a), and the first observation of two merg- ing neutron stars (Abbott et al. 2017a). The first ob- servation of two merging neutron stars was also a mul- timessenger event accompanied by emission across the electromagnetic (EM) spectrum (Abbott et al. 2017b; Margutti & Chornock 2021). The continued discovery of CBCs by the Advanced GW network in O4 and beyond promises to reveal new information about the formation pathways of compact binaries and the physics of their evolution. While GW observations have enabled detailed charac- terization of the population of stellar-mass compact ob- ject binary mergers overall (e.g., Abbott et al. 2023b), the small number of observed mergers at the low-mass end of the black hole mass spectrum leads to consider- able uncertainty in this region of the mass distribution. Dynamical mass measurements of X-ray binary systems within the Milky Way suggest a paucity of compact ob- jects with masses between ∼ 3–5 M⊙, and hence a lower mass gap that divides the population of neutron stars (with masses less than ∼ 3 M⊙; Rhoades & Ruffini 1974; Kalogera & Baym 1996) and stellar-mass black holes (observed to have masses above 5 M⊙; Bailyn et al. 1998; Ozel et al. 2010; Farr et al. 2011b). Although a number of recent observations of non-interacting binary
  • 2. 2 systems (Thompson et al. 2019; Jayasinghe et al. 2021), radio pulsar surveys (Barr et al. 2024), and GW obser- vations (Abbott et al. 2020c, 2023b) have found hints of compact objects residing in the lower mass gap, GW observations have yet to quantify the extent and poten- tial occupation of this gap (Fishbach et al. 2020; Farah et al. 2022; Abbott et al. 2023b). Here we report on the compact binary merger signal GW230529 181500, henceforth abbreviated as GW230529, which was detected by the LIGO Livingston observatory on 2023 May 29 at 18:15:00 UTC; all other observatories were either offline or did not have the sen- sitivity required to observe this signal. We find that the compact binary source of GW230529 had component masses of 3.6+0.8 −1.2 M⊙ and 1.4+0.6 −0.2 M⊙ (all measurements are reported as symmetric 90% credible intervals around the median of the marginalized posterior distribution with default uniform priors, unless otherwise specified). Although we cannot definitively determine the nature of the higher-mass (primary) compact object in the bi- nary system, if we assume that all compact objects with masses below current constraints on the maximum neu- tron star mass are indeed neutron stars, the most prob- able interpretation for the source of GW230529 is the coalescence between a 2.5–4.5 M⊙ black hole and a neu- tron star. GW230529 provides further evidence that a population of compact objects exists with masses be- tween the heaviest neutron stars and lightest black holes observed in the Milky Way. Furthermore, if the source of GW230529 was a merger between a neutron star and a black hole, its masses are significantly more symmetric than the neutron star–black holes (NSBHs) previously observed via GWs (Abbott et al. 2023a), which increases the expected rate of NSBHs that may be accompanied by an EM counterpart. We report on the status of the detector network at the time of GW230529 in Section 2 and provide details of the detection in Section 3. In Section 4 we present es- timates of the source properties along with a discussion of the inferred masses, spins, tidal effects, and consis- tency of the signal with general relativity. We provide updated constraints on merger rates and the inferred properties of the compact binary and NSBH popula- tions as well as population-informed posteriors on source properties in Section 5. Section 6 provides analysis and interpretation of the physical nature of the source com- ponents. Implications for multimessenger astrophysics and the formation of low-mass black holes are in Sec- tions 7 and 8, respectively. Section 9 summarizes our findings. Data from the analyses in this work are avail- able on Zenodo (Abbott et al. 2024a). 2. OBSERVATORY STATUS AND DATA QUALITY At the time of GW230529 (2023 May 29 18:15:00.7 UTC), LIGO Livingston was in observing mode; LIGO Hanford was offline, having gone out of observing mode one hour and thirty minutes prior to the detection. The Virgo observatory was undergoing upgrades and was not operational at the time of the detection. The KAGRA observatory was in observing mode, but its sensitivity was insufficient to impact the analysis of GW230529. Hence, only the data from the LIGO Livingston obser- vatory are used in the analysis of GW230529. LIGO Livingston was observing with stable sensitiv- ity for ≃ 66 hours up to and including the time of the GW signal. At the time of the detection, the sky- averaged binary neutron star (BNS) inspiral range was ≃ 150 Mpc. From the start of O4 until this event, the LIGO Livingston BNS inspiral range (Chen et al. 2021a) varied between 140–160 Mpc, a 4.5–19.4% increase com- pared to the median BNS range in O3 (Buikema et al. 2020; Abbott et al. 2023a). Additional details on up- grades to the LIGO observatories for O4 can be found in Appendix A. The Advanced LIGO observatories are laser interfer- ometers that measure strain (Aasi et al. 2015). The ob- servatories are calibrated via photon radiation pressure actuation. An amplitude-modulated laser beam is di- rected onto the end test masses inducing a known change in the arm length from the equilibrium position (Karki et al. 2016; Viets et al. 2018). For the strain data used in the GW230529 analysis, the maximum 1σ bounds on calibration uncertainties at LIGO Livingston were 6% in amplitude and 6.5◦ in phase for the frequency range 20–2048 Hz. Detection vetting procedures similar to those of past GW candidates (Davis et al. 2021; Abbott et al. 2016b), when applied to GW230529, find no evidence that in- strumental or environmental artifacts (Helmling-Cornell et al. 2023; Nguyen et al. 2021; Effler et al. 2015) could have caused GW230529. We find no evidence of tran- sient noise that is likely to impact the recovery of the GW signal in the 256 s LIGO Livingston data segment containing the signal. 3. DETECTION OF GW230529 GW230529 was initially detected in low latency in data from the LIGO Livingston observatory. The sig- nal was detected independently by three matched-filter search pipelines: GstLAL (Messick et al. 2017; Sachdev et al. 2019; Hanna et al. 2020; Cannon et al. 2021; Ew- ing et al. 2023; Tsukada et al. 2023), MBTA (Adams et al. 2016; Aubin et al. 2021) and PyCBC (Allen et al. 2012; Allen 2005; Dal Canton et al. 2021; Usman et al.
  • 3. 3 2016; Nitz et al. 2017; Davies et al. 2020). Although GW230529 occurred when only a single detector was observing, it was detected by all three pipelines with high significance, and stands out from the background distribution of noise triggers. More details are given in Appendix B. All three pipelines have a similar matched-filter-based approach to identify GW candidates but differ in the details of implementation. Each pipeline begins by per- forming a matched-filtering analysis on the data from the observatory with a bank of GW templates (Sakon et al. 2024; Roy et al. 2019; Florian et al. 2024). Times of high signal-to-noise ratio (S/N) are identified, after which each pipeline performs its own set of signal con- sistency tests, combines them with the S/N to make a single ranking statistic for each candidate GW event, and calculates a false alarm rate (FAR) by comparing the ranking statistic of the candidate with the back- ground distribution. The FAR is the expected rate of triggers caused by noise with a ranking statistic greater than or equal to that of the candidate. For each pipeline, this procedure can be done in two modes: a low-latency or online mode, and an offline mode. In the online mode, the pipelines only use the background information available at the time of a candi- date to estimate its significance, along with low-latency data-quality information. In the offline mode, pipelines use more background information gathered from sub- sequent observing times to estimate the significance of candidates and use more refined data-quality informa- tion. The offline mode enables more robust and repro- ducible results at the cost of greater latency. In both cases, the background distribution is extrap- olated to higher significances. This enables the inverse FAR to be greater than the time for which the back- ground was collected. Pipelines have differing extrapo- lation methods, and differing methods for calculating the FAR of a single-detector GW candidates, details of which can be found in Appendix C. These differ- ing methods can cause the FARs reported by different pipelines for the same candidate to vary to a signifi- cant degree, as seen in the case of GW230529. How- ever, all three pipelines recover a nearly identical S/N for GW230529, as expected for an astrophysical signal with a high match to the search templates. This, in con- cert with the fact that the inverse FARs from the offline analyses of all pipelines are much greater than the dura- tion of the first half of the fourth observing run (O4a), makes it highly likely that GW230529 is of astrophysi- cal origin. Table 1 shows the online S/N, online inverse FAR, and offline inverse FAR for each search pipeline. Table 1. Properties of the detection of GW230529 from each search pipeline. Significance is measured by the inverse of the FAR. GstLAL MBTA PyCBC Online S/N 11.3 11.4 11.6 Online inverse FAR (yr) 1.1 1.1 160.4 Offline inverse FAR (yr) 60.3 >1000 >1000 4. SOURCE PROPERTIES The source properties of GW230529 are inferred us- ing a Bayesian analysis of the data from the LIGO Liv- ingston observatory. We analyze 128 s of data including frequencies in the range of 20–1792 Hz in the calculation of the likelihood. To describe the detector noise, we as- sume a noise power spectral density (PSD) given by the median estimate provided by BayesWave (Littenberg & Cornish 2015; Cornish & Littenberg 2015; Cornish et al. 2021). We use the Bilby (Ashton et al. 2019; Romero-Shaw et al. 2020) or Parallel Bilby (Smith et al. 2020) inference libraries to generate samples from the posterior distribution of the source parameters us- ing a nested sampling (Skilling 2006) algorithm, as im- plemented in the Dynesty software package (Speagle 2020). Given the uncertain nature of the compact objects of the source, we analyze GW230529 using a range of wave- form models that incorporate a number of key physi- cal effects. For our primary analysis, we employ binary black hole (BBH) waveform models that include higher- order multipole moments, the effects of spin-induced or- bital precession, and allow for spin magnitudes on both components up to the Kerr limit, but do not include tidal effects on either component. Systematic errors in inferred source properties due to waveform modeling may be significant for NSBH systems (Huang et al. 2021). We mitigate these ef- fects by combining the posteriors inferred using two dif- ferent signal models: the phenomenological frequency- domain model IMRPhenomXPHM (Pratten et al. 2020; Garcı́a-Quirós et al. 2020; Pratten et al. 2021), and a time-domain effective-one-body model SEOB- NRv5PHM (Khalil et al. 2023; Pompili et al. 2023; Ramos-Buades et al. 2023; van de Meent et al. 2023). The posterior samples obtained independently using the two signal models are broadly consistent. Unless other- wise noted, we present results throughout this work ob- tained by an equal-weight combination of the posterior
  • 4. 4 Table 2. Source properties of GW230529 from the pri- mary combined analysis (BBH waveforms, high-spin, default priors). We report the median values together with the 90% symmetric credible intervals at a reference frequency of 20 Hz. Primary mass m1/M⊙ 3.6+0.8 −1.2 Secondary mass m2/M⊙ 1.4+0.6 −0.2 Mass ratio q = m2/m1 0.39+0.41 −0.12 Total mass M/M⊙ 5.1+0.6 −0.6 Chirp mass M/M⊙ 1.94+0.04 −0.04 Detector-frame chirp mass (1 + z)M/M⊙ 2.026+0.002 −0.002 Primary spin magnitude χ1 0.44+0.40 −0.37 Effective inspiral-spin parameter χeff −0.10+0.12 −0.17 Effective precessing-spin parameter χp 0.40+0.39 −0.30 Luminosity distance DL/Mpc 201+102 −96 Source redshift z 0.04+0.02 −0.02 samples from both models under the default priors de- scribed in Appendix D. Our measurements of key source parameters for GW230529 are presented in Table 2. Analysis details and results from other waveform mod- els we consider are reported in Appendix D; we find that the key conclusions of the analyses presented here are not sensitive to the choice of signal model. In par- ticular, the use of BBH models is validated by com- parison to waveform models that include tidal effects, finding no evidence that the BNS or NSBH models are preferred, consistent with previous observations (Abbott et al. 2021a). This is expected given the moderate S/N with which GW230529 was detected (Huang et al. 2021). The analysis of GW230529 indicates that it is an asymmetric compact binary with a mass ratio q = m2/m1 = 0.39+0.41 −0.12 and source component masses m1 = 3.6+0.8 −1.2 M⊙ and m2 = 1.4+0.6 −0.2 M⊙. The primary is consistent with a black hole that resides in the lower mass gap (3 M⊙ ≲ m1 ≲ 5 M⊙; Ozel et al. 2010; Farr et al. 2011b), with a mass < 5 M⊙ at the 99% credible level. The posterior distribution on the mass of the secondary is peaked around ∼ 1.4 M⊙ with an extended tail beyond 2 M⊙, such that P(m2 > 2 M⊙) = 5%. The mass of the secondary is con- sistent with the distribution of known neutron star masses, including Galactic pulsars (Antoniadis et al. 2016; Alsing et al. 2018; Özel & Freire 2016; Farrow et al. 2019) and extragalactic GW observations (Landry & Read 2021; Abbott et al. 2023b). Figure 1 shows Figure 1. The one- and two-dimensional posterior probability distributions for the component masses of the source binary of GW230529 (teal). The contours in the main panel denote the 90% credible regions with vertical and horizontal lines in the side panels denoting the 90% credible interval for the marginalized one-dimensional pos- terior distributions. Also shown are the two O3 NSBH events GW200105 162426 and GW200115 042309 (orange and blue respectively; Abbott et al. 2021a) with FAR < 0.25 yr−1 (Abbott et al. 2023a), the two confident BNS events GW170817 and GW190425 (pink and green respec- tively; Abbott et al. 2017a, 2019a, 2020a, 2024b), as well as GW190814 (red; Abbott et al. 2020c, 2024b) where the sec- ondary component may be a black hole or a neutron star. Lines of constant mass ratio are indicated by dotted gray lines. The grey shaded region marks the 3–5 M⊙ range of primary masses. The NSBH events and GW190814 use combined posterior samples assuming a high-spin prior anal- ogous to those presented in this work. The BNS events use high-spin IMRPhenomPv2 NRTidal (Dietrich et al. 2019a) samples. the component mass posteriors of GW230529 relative to other BNSs (GW170817 and GW190425) and NSBHs (GW200105 162426 and GW200115 042309, henceforth abbreviated as GW200105 and GW200115) observed by the LVK as well as GW190814 (Abbott et al. 2017a, 2020a,c, 2021a). To capture dominant spin effects on the GW signal, we present constraints on the effective inspiral spin χeff , which is defined as a mass-weighted projection of the spins along the unit Newtonian orbital angular momen- tum vector L̂N (Damour 2001; Racine 2008; Ajith et al.
  • 5. 5 Figure 2. Selected source properties of GW230529. The plot shows the one-dimensional (diagonal) and two- dimensional (off-diagonal) marginal posterior distributions for the primary mass m1, the mass ratio q, and the spin component parallel to the orbital angular momentum χ1,z ≡ χ1 · L̂N. The shaded regions denote the posterior proba- bility with the solid (dashed) curves marking the 50% and 90% credible regions for the posteriors determined using a high spin (low spin) prior on the secondary of χ2 < 0.99 (χ2 < 0.05). The vertical lines in the one-dimensional marginal posteriors mark the 90% credible intervals. 2014), χeff = m1 M χ1 + m2 M χ2 · L̂N, (1) where the dimensionless spin vector χi of each compo- nent is related to the spin angular momentum Si by χi = cSi/(Gm2 i ). If χeff is negative, it indicates that at least one of the spin component projections must be anti-aligned with respect to the orbital angular momen- tum, i.e., χi,z ≡ χi · L̂N 0. We measure an effective inspiral spin of χeff = −0.10+0.12 −0.17, which is consistent with a binary in which one of the spin components is anti-aligned or a binary with negligible spins. The mea- surement is primarily driven by the spin component of the primary compact object χ1,z = −0.11+0.19 −0.35, with a probability that χ1,z 0 of 83%. However, there is a degeneracy between the measured masses and spins of the binary components such that more comparable mass ratios correlate to more negative values of χeff (Cutler Flanagan 1994) for this system. We show the correlation between χ1,z and the mass ratio and primary mass in Figure 2, with more negative values of χ1,z correspond- ing to more symmetric mass ratios and smaller primary masses. The secondary spin is only weakly constrained and broadly symmetric about 0, χ2,z = −0.03+0.43 −0.52. We find no evidence for precession, with the posteriors on the effective precessing spin χp (Schmidt et al. 2015) being uninformative. The presence of a neutron star in a compact binary im- prints tidal effects onto the emitted GW signal (Flana- gan Hinderer 2008). The strength of this interaction is governed by the tidal deformability of the neutron star, which quantifies how easily the star will be deformed in the presence of an external tidal field. In contrast, the tidal deformability of a black hole is zero (Binnington Poisson 2009; Damour Nagar 2009; Chia 2021), of- fering a potential avenue for distinguishing between a black hole and a neutron star. We investigate the tidal constraints for both the primary and secondary com- ponents using waveform models that account for tidal effects (Dietrich et al. 2019a; Matas et al. 2020; Thomp- son et al. 2020a), which do not qualitatively change the mass and spin conclusions discussed above. Irrespec- tive of whether we analyze GW230529 with a NSBH model that assumes only the tidal deformability of the primary compact object to be zero or a BNS model that includes the tidal deformability of both objects, we find the tidal deformability of the secondary object to be unconstrained. The dimensionless tidal deformability of the primary peaks at zero, consistent with a black hole. The constraints on this parameter are also consistent with dense matter equation of state (EoS) predictions for neutron stars in this mass range. We also perform parametrized tests of the GW phase evolution to verify whether GW230529 is consistent with general relativity and find no evidence of inconsisten- cies. More detailed information on tidal deformability analyses and testing general relativity can be found in Appendix E.3 and Appendix F, respectively. 5. IMPACT OF GW230529 ON MERGER RATES POPULATIONS We provide a provisional update to the NSBH merger rate reported in our earlier studies (Abbott et al. 2021a, 2023b) by incorporating data from the first two weeks of O4a using two different methods. In the first, event- based approach, we consider GW230529 to be represen- tative of a new class of CBCs and assume its contribu- tion to the total number of NSBH detections to be a sin- gle Poisson-distributed count (Kim et al. 2003; Abbott et al. 2021a) over the span of time from the beginning of the first observing run (O1) through the first two weeks of O4a. We find the rate of GW230529-like mergers to be R230529 = 55+127 −47 Gpc−3 yr−1 . When computing the
  • 6. 6 Figure 3. Posterior on the merger rates of NSBH systems. The solid and dashed lines represent the broad population- based rate calculation and the event-based rate calculation, respectively. rates of the significant NSBH events in O3 detected with FAR 0.25 yr−1 (Abbott et al. 2021a, 2023a) using the same method, we find a total event-based NSBH merger rate of RNSBH = 85+116 −57 Gpc−3 yr−1 . Using this selec- tion criterion, the same as Abbott et al. (2023b), the population of NSBH mergers includes GW200105 and GW200115; we do not include GW190814, as its source binary is most probably a BBH (Abbott et al. 2020c; Essick Landry 2020; Abbott et al. 2023b). For the second, broad population-based approach, we consider GW200105, GW200115, and GW230529 to be members of a single CBC class, together with an ensem- ble of less significant candidates. The definition of this class is determined by a simple cut on masses and spins resulting in a NSBH-like region of parameter space. We aggregate data from all the triggers found by GstLAL from the beginning of O1 through the first two weeks of O4a, assess their impact on the estimated merger rates of NSBHs while also accounting for the possibility that some of them are of terrestrial origin (Farr et al. 2015; Kapadia et al. 2020), and update the NSBH merger rate obtained at the end of O3 (Abbott et al. 2023a) to RNSBH = 94+109 −64 Gpc−3 yr−1 . Further details regarding the classification of triggers in the population-based rate method can be found in Appendix G. We show updates to both the event-based and population-based NSBH rate constraints in Fig- ure 3. The event-based rate estimates highlight that GW230529-like systems merge at a similar (or poten- tially higher) rate to the more asymmetric NSBHs iden- tified in GWTC-3. The population-based rate estimate is more representative of the full NSBH merger rate as it includes less significant GW events in the data. Both of our updated estimates are consistent with the find- ings of Abbott et al. (2021a) within the measurement uncertainties. Further details about rate estimates can be found in Appendix G. In addition to updates to the overall merger rate of NSBHs, we also study the impact of GW230529 on the mass and spin distributions of the compact binary pop- ulation as inferred from GWTC-3 (Abbott et al. 2023b). We employ hierarchical Bayesian inference to marginal- ize over the properties of individual events and infer the parameters of a given population model (e.g., Thrane Talbot 2019; Mandel et al. 2019; Vitale et al. 2020). The updates to population model results in this work are pro- visional because they only include one GW signal from O4a, although the biases resulting from this selection will not be severe since GW230529 occurred near the start of the observing run. We quantify this by compar- ing the event-based rate estimate (which accounts for O4a sensitivity to compute its detectable time–volume) with the NSBH rates attained by the various population analyses considered in this work, finding that they are consistent with each other. We use three different population models in our anal- ysis. The first two models consider the population of compact-object binaries as a whole without distinguish- ing by source classification, using either the parameter- ized Power law + Dip + Break model (Fishbach et al. 2020; Farah et al. 2022; Abbott et al. 2023b) or the non-parametric Binned Gaussian Process model (Mohite 2022; Ray et al. 2023b; Abbott et al. 2023b). The Power law + Dip + Break model is designed to search for a separation in masses between neutron stars and black holes by explicitly allowing for a dip in the component mass distribution. The Binned Gaussian Process model is designed to capture the structure of the mass distribution with minimal assump- tions about the population. The broad CBC population analyses include all candidates reported in GWTC-3 with FAR 0.25 yr−1 , the same selection criterion used in Abbott et al. 2023b (see Table 1 therein). The third model we investigate (NSBH-pop; Biscoveanu et al. 2022) considers only the population of NSBH mergers with FAR 0.25 yr−1 . NSBH-pop is a parametric model designed to constrain the population distributions of NSBH masses and black hole spin magnitudes. This model assumes all analyzed events have a black hole primary and neutron star secondary; we do not include GW190814 in this analysis. Further details regarding the population model parameterizations and priors can be found in Appendix H.
  • 7. 7 Figure 4. The differential merger rate of NSBH systems as a function of black hole masses (solid curves: mean; shaded regions: 90% credible interval) and minimum black hole mass (dashed lines: 90% credible interval) using the NSBH-pop model with (teal) and without (grey) GW230529. The minimum black hole mass mBH,min is a parameter of the NSBH-pop population model, see Table 7. While the median rate is always inside the credible region, the mean can be outside the credible region. The inclusion of GW230529 in our population analyses has several effects on the inferred properties of NSBH systems and the CBC population as a whole. The inferred minimum mass of black holes in the NSBH population decreases with the inclusion of GW230529. The mass spectrum of black holes in the NSBH population with and without GW230529 inferred using the NSBH-pop model is shown in Figure 4. As the source of GW230529 is the NSBH with the small- est black hole mass observed to date, the minimum mass of black holes in NSBH mergers shows a sig- nificant decrease with the inclusion of this candidate: mmin,BH = 3.4+1.0 −1.2 M⊙ with GW230529 compared to mmin,BH = 6.0+1.8 −3.2 M⊙ without. In contrast, the pa- rameter that governs the lower edge of the dip feature in the Power law + Dip + Break model, which rep- resents the minimum black hole mass in the CBC pop- ulation, does not shift significantly with the inclusion of GW230529. This difference is because the Power law + Dip + Break model makes no assumptions about the classification of the components and there- fore does not enforce sharp features at the edges of each sub-population, meaning that the source of GW230529 is not necessarily a NSBH in this model. However, the Binned Gaussian Process and Power law + Dip + Break models are designed to capture the structure of the full compact binary mass spectrum; because they do not assign a source classification to either of the bi- nary components, features present in these population models can have differing astrophysical interpretations from the NSBH-pop model. GW230529 increases the inferred rate of compact bi- nary mergers with a component in the 3–5 M⊙ range. A region of interest in the mass distribution is the border between the masses of neutron stars and black holes. We choose ∼ 3–5 M⊙ to represent the nominal gap between these populations. In Figure 5 we show the posterior on the rate of mergers with one or both component masses in the 3–5 M⊙ range, with and without GW230529. For the Power law + Dip + Break model there is a small increase in the merger rate within this mass range, Rgap = 24+28 −16 Gpc−3 yr−1 with GW230529 ver- sus Rgap = 17+25 −14 Gpc−3 yr−1 without. For the Binned Gaussian Process model there is a larger increase in the merger rate, Rgap = 33+89 −29 Gpc−3 yr−1 with GW230529 versus Rgap = 7.5+46.4 −6.5 Gpc−3 yr−1 without. The differing degree of change between the two models is due to different assumptions for the mass ratio distri- bution of merging compact binaries as well as the po- tential dip in the merger rate at low black hole masses built into the Power law + Dip + Break model. Binned Gaussian Process does not fit for a specific pairing function, while Power law + Dip + Break assumes the same mass ratio distribution throughout the whole population of CBCs. As most observed BBHs favor equal masses, any population model conditioned on those observations should also favor equal masses in the BBH mass range. The implicit assumptions within the Power law + Dip + Break model require this preference to be imposed for all masses, including rela- tively low-mass systems like GW230529. However, the assumptions in Binned Gaussian Process do not broadcast this preference as strongly across different
  • 8. 8 Figure 5. Posterior on the merger rate of binaries with one or both components between 3–5 M⊙. The solid curves show the results from the Binned Gaussian Process analysis and the dashed curves show the results from the Power law + Dip + Break analysis. Both models analyze the full black hole and neutron star mass distribution. The teal and grey curves show the analysis results with and without GW230529, respectively. mass scales and therefore may support more asymmet- ric mass ratios at lower masses. Regardless of the mass ratio distribution assumptions made by each model, we find that the inclusion of GW230529 provides further evidence that the ∼ 3–5 M⊙ region is not completely empty. GW230529 is consistent with the population inferred from previously observed CBCs candidates. In Figure 6, we show the population distributions of the full black hole and neutron star mass spectrum for the primary component of compact binary mergers using the Binned Gaussian Process (top panel) and Power law + Dip + Break (bottom panel) population models. We qualitatively see that GW230529 is not an outlier with respect to the masses of previously-observed compact object binaries because the inclusion of GW230529 in the population does not significantly alter the full- population posterior constraints. This differs from the detection of GW190814, which was an outlier with re- spect to the rest of the observed BBH population at the time due to its small secondary mass (Essick et al. 2022). The observation of GW190814 strongly suggested the re- gion between the masses of neutron stars and black holes was populated (Abbott et al. 2023b), a conclusion that is strengthened with the detection of GW230529 (even though it is not an outlier). The component masses inferred for GW230529 differ across differing population-informed priors. In Figure 7, Figure 6. The differential binary merger rate as a function of the mass of the primary component using the Binned Gaussian Process model (top panel) and the Power law + Dip + Break model (bottom panel) for the full compact binary population (solid curves: mean; shaded regions: 90% credible interval) with (teal) and without (grey) GW230529. we show the mass and spin posteriors obtained using priors informed by each of the population models con- sidered in this work. The priors informed by the NSBH- pop model prefer unequal mass ratios and small black hole spins; they suppress the extended posterior tail out to equal masses and anti-aligned spins. The Binned Gaussian Process model also pulls the posteriors to more asymmetric mass ratios and has less support for anti-aligned spins. As shown in the top panel of Fig- ure 6, the merger rate density inferred using the Binned Gaussian Process model is nearly flat across the re- gion of parameter space covered by GW230529, mean- ing that the priors informed by this population model have less of an impact on the shape of the posterior compared to the parameterized models considered. Un- like the NSBH-pop model, the Power law + Dip + Break model has a sharp drop in the merger rate above
  • 9. 9 Figure 7. Posterior distributions of GW230529 under vari- ous prior assumptions. The solid teal curve shows the poste- rior distributions using the default high-spin priors described in Appendix D. The various dashed and dotted curves show posteriors obtained using population priors based on the NSBH-pop model (orange), Binned Gaussian Process (blue) and Power law + Dip + Break (red) models. 3 M⊙. This sharp feature results in the posterior on the primary component being pulled below 3 M⊙ as well as the posterior on the secondary being pulled to higher masses. The Binned Gaussian Process model has a similar feature, although it is closer to 2 M⊙ and there- fore too low to significantly affect the mass estimates for this system. The Power law + Dip + Break model also assumes the same preference for equal-mass systems across the entire mass spectrum, and thus, given that the majority of the CBC population is consistent with symmetric mass ratios, infers that the GW230529 binary components are more similar in mass. The combination of the drop in the differential merger rate and the pref- erence for symmetric mass ratios increases the support for more extreme spins oriented in the hemisphere oppo- site the orbital angular momentum. From these models we find that the binary source of GW230529 either has asymmetric components with low values of χeff , or has components that are similar in mass with χeff ∼ −0.3. These results highlight that the choice of prior has a sig- nificant impact on the inferred masses and spins of the GW230529 source, and hence the inferred nature of the binary components. We assess the nature of the compo- nents further in Section 6. More details on the popula- tion prior reweighting are given in Appendix H.4. 6. NATURE OF THE COMPACT OBJECTS IN THE GW230529 BINARY Without clear evidence for or against tidal effects in the signal, the physical nature of the compact objects in the GW230529 source binary can be assessed by com- paring the measured masses and spins of each compo- nent with the maximum masses and spins of neutron stars allowed by previous observational data. However, statistical uncertainties in component masses make it especially difficult to determine whether compact ob- jects with masses between ∼ 2.5–5 M⊙ are consistent with being black holes or neutron stars (Hannam et al. 2013; Littenberg et al. 2015). Nevertheless, we assess the nature of the source components by marginaliz- ing over our uncertainties in the masses and spins of GW230529, in the population of merging binaries, and in the supranuclear EoS, to compute the posterior prob- ability that each component had a mass and spin less than the maximum mass and spin supported by the EoS. We follow the procedure introduced in the context of GW190814 (Abbott et al. 2020c; Essick Landry 2020), which relied on only the maximum neutron star mass, and has subsequently been extended to include the effects of spin (Abbott et al. 2020c, 2021a, 2023b). Our analysis provides only an upper limit on the prob- ability that an object is a neutron star, as it assumes that all objects consistent with the maximum mass and spin of a neutron star are indeed neutron stars (Essick Landry 2020). To assess the nature of the component masses of the GW230529 source, we consider two versions of an astrophysically-agnostic population model that is uni- form in source-frame component masses and spin mag- nitudes and isotropic in spin orientations: one with com- ponent spin magnitudes χi ≡ |χi| that are allowed to be large (χ1, χ2 ≤ 0.99) and one where they are restricted a priori to be small (χ1, χ2 ≤ 0.05). We also consider the Power law + Dip + Break population model (see Appendix H.2) fit to the GW candidates from GWTC- 3 (Abbott et al. 2023a); including GW230529 in the population model does not significantly affect the re- sults. For each population, we marginalize over the un- certainty in the maximum neutron star mass conditioned on the existence of massive pulsars and previous GW ob- servations (Landry et al. 2020) using a flexible Gaussian process (GP) representation of the EoS (Landry Es- sick 2019; Essick et al. 2020b). More information on the EoS choices can be found in Appendix I. Table 3 reports the probability that each component of the merger is consistent with a neutron star. In gen- eral, we find that the secondary is almost certainly con- sistent with a neutron star, and the primary is most
  • 10. 10 Table 3. Probabilistic source classification based on consistency of component masses with the maximum neutron star mass and spin. All estimates marginalize over uncertainty in the masses, spins, and redshift of the source as well as uncertainty in the astrophysical population and the EoS. We consider three population models: two distributions that use astrophysically-agnostic priors and consider either large spins (χ1, χ2 ≤ 0.99) or small spins (χ1, χ2 ≤ 0.05), and a population prior using the Power law + Dip + Break model fit with only the events from GWTC-3 (Abbott et al. 2023b). We use an EoS posterior conditioned on massive pulsars and GW observations (Landry et al. 2020). All errors approximate 90% uncertainty from the finite number of Monte Carlo samples used with the exception of the low-spin results for which we only place an upper or lower bound. χ1, χ2 ≤ 0.99 χ1, χ2 ≤ 0.05 Power law + Dip + Break P(m1 is NS) (2.9 ± 0.4)% 0.1% (8.8 ± 2.8)% P(m2 is NS) (96.1 ± 0.4)% 99.9% (98.4 ± 1.3)% probably a black hole. However, when incorporating information from the Power law + Dip + Break population model, we find that there is a ∼ 1 in 10 chance that the primary is consistent with a neutron star. If we further relax the fixed spin assumptions im- plicit within the Power law + Dip + Break model for objects with masses ≤ 2.5 M⊙ from χi ≤ 0.4 to χi ≤ 0.99 (see Appendix H.2), we can find probabilities as high as P(m1 is NS) = (27.3 ± 3.8)%. This ambigu- ity is similar to the secondary component of GW190814 (2.50 ≤ m2/M⊙ ≤ 2.67), which is consistent with a neu- tron star if it was rapidly spinning (e.g., Essick Landry 2020; Abbott et al. 2020c; Most et al. 2020a). The differences observed between population models primarily reflect the uncertainty in the mass ratio and spins of the GW230529 source. For example, incorporat- ing the Power law + Dip + Break population model as a prior updates the posterior for m1 from 3.6+0.8 −1.2 M⊙ to 2.7+0.9 −0.4 M⊙. Additional observations of compact ob- jects in or near the lower mass gap may clarify the com- position of GW230529 by further constraining the ex- act shape of the distribution of compact objects below ∼ 5 M⊙ or the supranuclear EoS. 7. IMPLICATIONS FOR MULTIMESSENGER ASTROPHYSICS In NSBH mergers, the neutron star can either plunge directly into the black hole or be tidally disrupted by its gravitational field. Tidal disruption would leave some remnant baryonic material outside the black hole that could potentially power a range of EM counterparts in- cluding a kilonova (Lattimer Schramm 1974; Li Paczynski 1998; Tanaka Hotokezaka 2013; Tanaka et al. 2014; Fernández et al. 2017; Kawaguchi et al. 2016) or a gamma-ray burst (Mochkovitch et al. 1993; Janka et al. 1999; Paschalidis et al. 2015; Shapiro 2017; Ruiz et al. 2018). The conditions for tidal disruption are de- termined by the mass ratio of the binary, the compo- nent of the black hole spin aligned with the orbital an- gular momentum, and the compactness of the neutron star (Pannarale et al. 2011; Foucart 2012; Foucart et al. 2018; Krüger Foucart 2020). While the disruption probability of the neutron star in GW230529 can be in- ferred based on the binary parameters, we are unlikely to directly observe the disruption in the GW signal with- out next-generation observatories (Clarke et al. 2023). We use the ensemble of fitting formulae collected in Biscoveanu et al. (2022) including the spin-dependent properties of neutron stars (Foucart et al. 2018; Cipol- letta et al. 2015; Breu Rezzolla 2016; Most et al. 2020b) to constrain the remnant baryon mass outside the final black hole following GW230529, assuming it was produced by a NSBH merger. We additionally marginalize over the uncertainty in the GP-EoS re- sults obtained using the method introduced in Sec- tion 6 (Legred et al. 2021, 2022). Using the high-spin combined posterior samples obtained with default pri- ors, we find a probability of neutron star tidal disruption of 0.1, corresponding to an upper limit on the remnant baryon mass produced in the merger of 0.052 M⊙ at 99% credibility. The low-secondary-spin priors (χ2 0.05) yield a tidal disruption probability and remnant baryon mass upper limit of 0.042 and 0.011 M⊙, respectively. A rapidly spinning neutron star is less compact than a slowly spinning neutron star of the same gravitational mass under the same EoS. This decrease in compactness leads to a larger disruption probability and a larger rem- nant baryon mass following the merger, explaining the trend we see when comparing the results obtained un- der the low-secondary- and high-spin priors. The source binary of GW230529 is the most probable of the con- fident NSBHs reported by the LVK to have undergone tidal disruption because of the increased symmetry in its component masses. However, the exact value of the tidal disruption probability and the remnant baryon mass for this system are prior-dependent.
  • 11. 11 Figure 8. Posterior on the fraction of NSBH systems de- tected with GWs that may be EM bright, fEM-bright, de- pending on the threshold remnant mass required to power a counterpart, f(Mb rem Mb rem,min). The solid and dashed curves represent different values of the minimum remnant mass Mb rem,min. The teal and grey curves show the analysis results with and without GW230529, respectively. We can also gauge how the inclusion of GW230529 impacts estimates of the fraction of NSBH systems de- tected in GWs that may be accompanied by an EM counterpart, fEM-bright. Using the mass and spin dis- tributions inferred under the NSBH-pop population model described in Section 5, we find a 90% credi- ble upper limit on the fraction of NSBH mergers that may be EM-bright of fEM-bright ≤ 0.18 when includ- ing GW230529, an increase relative to fEM-bright ≤ 0.06 obtained when excluding GW230529 from the analysis. These estimates assume that any remnant baryon mass Mb rem,min ≥ 0 could power a counterpart, although the actual threshold value is astrophysically uncertain. Fig- ure 8 shows the posterior for fEM–bright with and with- out the inclusion of GW230529. While the exact value of fEM-bright depends on the assumed population model, the increase in fEM-bright for NSBHs upon the inclusion of GW230529 in the population is robust against mod- eling assumptions. Using these updated multimessenger prospects, we can infer the contribution of NSBH mergers to the pro- duction of heavy elements (Biscoveanu et al. 2022) and the generation of gamma-ray bursts (Biscoveanu et al. 2023). Assuming that all remnant baryon mass pro- duced in NSBH mergers is enriched in heavy elements via r-process nucleosynthesis (Lattimer Schramm 1974, 1976), we infer that NSBH mergers contribute at most 1.1 M⊙ Gpc−3 yr−1 to the production of heavy elements and that the rate of gamma-ray bursts with NSBH progenitors is at most 23 Gpc−3 yr−1 at 90% credibility. This likely represents a small fraction of all short gamma-ray bursts, for which astrophysical beaming-corrected rate estimates range from O(10 − 1000) Gpc−3 yr−1 (Mandel Broekgaarden 2022), and of the total r-process material produced by compact- object mergers (Côté et al. 2018; Chen et al. 2021b). No significant counterpart candidates have been re- ported for GW230529 (IceCube Collaboration 2023; Karambelkar et al. 2023; Lipunov et al. 2023; Longo et al. 2023; Lesage et al. 2023; Savchenko et al. 2023; Sugita et al. 2023a,b; Waratkar et al. 2023). This is un- surprising given that it was only observed by a single detector and hence was poorly localized on the sky. 8. ASTROPHYSICAL IMPLICATIONS Since the late 1990s, there have been claims about the existence of a mass gap between the maximum neutron star mass and the minimum black hole mass (∼ 3–5 M⊙) based on dynamical mass measurements of Galactic X- ray binaries (Bailyn et al. 1998; Ozel et al. 2010; Farr et al. 2011b). The lower edge of this purported mass gap depends on the maximum possible mass with which a neutron star can form in a supernova explosion, which cannot exceed the maximum allowed neutron star mass given by the EoS. Some EoSs support masses up to ∼ 3 M⊙ for nonrotating neutron stars (Mueller Serot 1996; Godzieba et al. 2021) and even larger masses for rotating neutron stars (Friedman Ipser 1987; Cook et al. 1994), although such large values are disfavored by the tidal deformability inferred for GW170817 (Abbott et al. 2019b) and Galactic observations (Alsing et al. 2018; Farr Chatziioannou 2020). The upper edge and extent of the mass gap depend on the minimum black hole mass that can form from stellar core collapse. How- ever, it remains an open question whether observational or evolutionary selection effects inherent to the detec- tion of Galactic X-ray binaries can lead to the observed gap in compact object masses (Fryer Kalogera 2001; Kreidberg et al. 2012; Siegel et al. 2023). In recent years, new EM observations have unveiled a few candidates in the ∼ 3 M⊙ region, mostly from non-interacting binary systems (Thompson et al. 2019; van den Heuvel Tauris 2020; Thompson et al. 2020b) and radio surveys for pulsar binary systems (Barr et al. 2024). Microlensing surveys do not support the existence of a mass gap but cannot exclude it ei- ther (Wyrzykowski et al. 2016; Wyrzykowski Man- del 2020). The LVK has already observed one compo- nent of a merger whose mass falls between the most massive neutron stars and least massive black holes observed in the Galaxy: the secondary component of
  • 12. 12 GW190814 (2.5–2.7 M⊙ at the 90% credible level; Ab- bott et al. 2020c, 2024b). The secondary components of the GW200210 092254 and GW190917 114630 source binaries also have support in the lower mass gap (Ab- bott et al. 2024b, 2023a), although their mass estimates are also consistent with a high-mass neutron star. Un- like GW230529, the primary components of all three of these binaries can be confidently identified as black holes. Overall, the existence of a mass gap between the most massive neutron stars and least massive black holes still stands as an open question in astrophysics. GW230529 is the first compact binary with a primary component that has a high probability of residing in the lower mass gap. Hence, GW230529 reinforces the con- clusion that the 3–5 M⊙ range is not completely empty (see Figure 5 in Section 5). However, the 3–5 M⊙ range may still be less populated than the surrounding regions of the mass spectrum. This conclusion is consistent with previous population analyses and rate estimates based on GWTC-3 (Abbott et al. 2023b). The formation of GW230529 raises a number of ques- tions. Given our current understanding of core collapse in massive stars (O’Connor Ott 2011; Janka 2012; Ertl et al. 2020), it is unlikely that the primary compo- nent formed via direct collapse because of its low mass, although stochasticity in the physical mechanisms that determine remnant mass may populate the low-mass end of the black hole mass spectrum (Mandel Müller 2020; Antoniadis et al. 2022). Formation by fallback is a vi- able scenario: recent numerical models of core-collapse supernovae suggest that the formation of 3–6 M⊙ black holes via substantial fallback is rare but still possible (e.g., Sukhbold et al. 2016; Ertl et al. 2020). One- dimensional hydrodynamical simulations of core collapse adopting pure helium star models predict that there is no empty gap, only a less populated region between 3–5 M⊙, with the lowest mass of black holes produced by prompt implosions starting at ≈ 6 M⊙ (Ertl et al. 2020). Another relevant parameter is the timescale for instability growth and launch of the core-collapse su- pernova; if this is long enough (≳ 200 ms), the proto- neutron star might accrete enough mass before the ex- plosion to become a mass-gap object (Fryer Kalogera 2001; Fryer et al. 2012). Compact binary population synthesis models that allow for longer instability growth timescales naturally produce merging NSBH systems with the primary component in the lower mass gap (Bel- czynski et al. 2012; Chattopadhyay et al. 2021; Zevin et al. 2020; Broekgaarden et al. 2021; Olejak et al. 2022). It may also be possible to form mass-gap objects through accretion onto a neutron star. If the first-born neu- tron star in the binary accretes enough material prior to the formation of the second-born compact object, it can trigger an accretion-induced collapse into a black hole, yielding a mass-gap object (Siegel et al. 2023). This scenario may be aided by super-Eddington accre- tion onto the first-born neutron star, which has been proposed to explain NSBHs with mass-gap black holes like the source of GW230529 (Zhu et al. 2023). Consid- ering the large number of uncertainties about the out- come of core-collapse supernovae (e.g., Burrows Var- tanyan 2021), the primary mass of GW230529 provides a piece of evidence to inform and constrain future models. Overall, astrophysical models in the past have preferen- tially adopted prescriptions that enforce the presence of a lower-mass gap (e.g., Fryer et al. 2012), and the in- ferred rate of GW230529-like systems urges a change of paradigm in such model assumptions. Alternatively, the primary component of GW230529 might be the result of the merger of two neutron stars. For instance, the 90% credible intervals for the remnant mass of GW190425 and the primary mass of GW230529 overlap (Abbott et al. 2020a). This may hint at a sce- nario where the primary component could either be the member of a former triple or quadruple system (Fra- gione et al. 2020; Lu et al. 2021; Vynatheya Hamers 2022; Gayathri et al. 2023), or the result of a dynami- cal capture in a star cluster (Clausen et al. 2013; Gupta et al. 2020; Rastello et al. 2020; Arca Sedda 2020, 2021) or AGN disk (Tagawa et al. 2021; Yang et al. 2020). This scenario was proposed for the formation of a com- pact object discovered in a binary with a pulsar in the globular cluster NGC 1851, which is measured to have a mass of 2.09–2.71 M⊙ at 95% confidence (Barr et al. 2024). However, dynamically-induced BNS merg- ers are predicted to be rare in dense stellar environments (O(10−2 ) Gpc−3 yr−1 ; e.g., Ye et al. 2020). Thus, the rate of mergers between a BNS merger remnant and a neutron star may be at least several orders of magnitude lower than the rate we infer for GW230529-like mergers, making this scenario improbable. Non-stellar-origin black hole formation scenarios such as primordial black holes (e.g., Clesse Garcia-Bellido 2022) remain a possibility. However, there are signifi- cant uncertainties in the predicted mass spectrum and merger rate of primordial black hole binaries, thus mak- ing it difficult to attribute a primordial origin to com- pact objects that have masses consistent with predic- tions from massive-star core collapse. Furthermore, re- sults from microlensing surveys indicate that primordial black hole mergers cannot be a dominant source of GWs in the local universe (Mroz et al. 2024). It has also been suggested that mergers apparently in- volving mass-gap objects could instead be gravitation-
  • 13. 13 ally lensed BNSs (Bianconi et al. 2023; Magare et al. 2023), with the lensing magnification making them ap- pear heavier and closer (Wang et al. 1996; Dai et al. 2017; Hannuksela et al. 2019). This scenario is diffi- cult to explicitly test in the absence of tidal informa- tion (Pang et al. 2020) or EM counterparts (Bianconi et al. 2023), but the expected relative rate of strong lens- ing is low at current detector sensitivities (Smith et al. 2023; Magare et al. 2023; Abbott et al. 2023c). Finally, we also find mild support for the possibility that the primary component is a neutron star rather than a black hole when considering the population-based Power law + Dip + Break prior that incorporates the potential presence of a gap at low black hole masses. In this case, GW230529 would be the most massive neu- tron star binary yet observed, with both components ≳ 2.0 M⊙, and have non-zero spins that are anti-aligned with the orbital angular momentum. The effective in- spiral spin of the BNSs in this scenario would differ significantly from BNS sources previously observed in GWs (Abbott et al. 2017a, 2020a) as well as those in- ferred for Galactic BNSs if they were to merge (Zhu et al. 2018). Spins oriented in the hemisphere opposite the bi- nary orbital angular momentum could be the result of supernova natal kicks (Kalogera 2000; Farr et al. 2011a; O’Shaughnessy et al. 2017; Chan et al. 2020) or spin-axis tossing (Tauris 2022) at birth. For example, one of the neutron stars in the binary pulsar system J0737–3039 is significantly misaligned with respect to both the spin of its companion and the orbital angular momentum of the binary system, which may require off-axis kicks (Farr et al. 2011a). Alternatively, isotropically-oriented com- ponent spins that result from random pairing in dynam- ical environments could lead to the significant spin mis- alignment (e.g., Rodriguez et al. 2016). 9. SUMMARY GW230529 is a GW signal from the coalescence of a 2.5–4.5 M⊙ compact object and a compact object con- sistent with neutron star masses. The more massive component in the merger provides evidence that com- pact objects in the hypothesized lower mass gap exist in merging binaries. Based on mass estimates of the two components in the merger and current constraints on the supranuclear EoS, we find the most probable inter- pretation of the GW230529 source to be a NSBH coales- cence. In this scenario, the source binary of GW230529 is the most symmetric-mass NSBH merger yet observed, and the primary component of the merger is the lowest- mass primary black hole (BH) observed in GWs to date. Because NSBHs with more symmetric masses are more susceptible to tidal disruption, the observation of GW230529 implies that more NSBHs than previously inferred may produce EM counterparts. However, we cannot rule out the contrasting scenario that the source of GW230529 consisted of two neutron stars rather than a neutron star and a black hole. In this case, the source of GW230529 would be the only BNS coalescence ob- served to have strong support for non-zero and anti- aligned spins, as well as the highest-mass BNSs system observed to date. Regardless of the true nature of the GW230529 source, it is a novel addition to the grow- ing population of CBCs observed via their GW emission and highlights the importance of continued exploration of the CBC parameter space in O4 and beyond. Strain data containing the signal from the LIGO Liv- ingston observatory is available from the Gravitational Wave Open Science Center.1 Specifically, we release the L1:GDS-CALIB STRAIN CLEAN AR channel, where the textttAR designation means the strain data is analy- sis ready; this strain channel was also released at the end of O3. Samples from the posterior distributions of the source parameters, hyperposterior distributions from population analyses, and notebooks for reproduc- ing all results and figures in this paper are available on Zenodo (Abbott et al. 2024a). The software packages used in our analyses are open-source. This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility fully funded by the National Science Foundation. The authors also gratefully acknowledge the support of the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construc- tion of Advanced LIGO and construction and opera- tion of the GEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Re- search Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Netherlands Organization for Scientific Research (NWO), for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowl- edge research support from these agencies as well as by the Council of Scientific and Industrial Research of In- dia, the Department of Science and Technology, India, the Science Engineering Research Board (SERB), In- dia, the Ministry of Human Resource Development, In- dia, the Spanish Agencia Estatal de Investigación (AEI), the Spanish Ministerio de Ciencia, Innovación y Univer- 1 https://doi.org/10.7935/6k89-7q62
  • 14. 14 sidades, the European Union NextGenerationEU/PRTR (PRTR-C17.I1), the Comunitat Autonòma de les Illes Balears through the Direcció General de Recerca, In- novació i Transformació Digital with funds from the Tourist Stay Tax Law ITS 2017-006, the Conselleria d’Economia, Hisenda i Innovació, the FEDER Opera- tional Program 2021-2027 of the Balearic Islands, the Conselleria d’Innovació, Universitats, Ciència i Societat Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de Catalunya, Spain, the Na- tional Science Centre of Poland and the European Union – European Regional Development Fund; Foundation for Polish Science (FNP), the Polish Ministry of Science and Higher Education, the Swiss National Science Foun- dation (SNSF), the Russian Foundation for Basic Re- search, the Russian Science Foundation, the European Commission, the European Social Funds (ESF), the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scot- tish Universities Physics Alliance, the Hungarian Scien- tific Research Fund (OTKA), the French Lyon Institute of Origins (LIO), the Belgian Fonds de la Recherche Scientifique (FRS-FNRS), Actions de Recherche Con- certées (ARC) and Fonds Wetenschappelijk Onderzoek – Vlaanderen (FWO), Belgium, the Paris Île-de-France Region, the National Research, Development and In- novation Office Hungary (NKFIH), the National Re- search Foundation of Korea, the Natural Science and Engineering Research Council Canada, Canadian Foun- dation for Innovation (CFI), the Brazilian Ministry of Science, Technology, and Innovations, the International Center for Theoretical Physics South American Insti- tute for Fundamental Research (ICTP-SAIFR), the Re- search Grants Council of Hong Kong, the National Nat- ural Science Foundation of China (NSFC), the Lever- hulme Trust, the Research Corporation, the National Science and Technology Council (NSTC), Taiwan, the United States Department of Energy, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN and CNRS for pro- vision of computational resources. This work was sup- ported by MEXT, JSPS Leading-edge Research Infras- tructure Program, JSPS Grant-in-Aid for Specially Pro- moted Research 26000005, JSPS Grant-in-Aid for Scien- tific Research on Innovative Areas 2905: JP17H06358, JP17H06361 and JP17H06364, JSPS Core-to-Core Pro- gram A. Advanced Research Networks, JSPS Grant-in- Aid for Scientific Research (S) 17H06133 and 20H05639, JSPS Grant-in-Aid for Transformative Research Areas (A) 20A203: JP20H05854, the joint research program of the Institute for Cosmic Ray Research, University of Tokyo, National Research Foundation (NRF), Comput- ing Infrastructure Project of Global Science experimen- tal Data hub Center (GSDC) at KISTI, Korea Astron- omy and Space Science Institute (KASI), and Ministry of Science and ICT (MSIT) in Korea, Academia Sinica (AS), AS Grid Center (ASGC) and the National Science and Technology Council (NSTC) in Taiwan under grants including the Rising Star Program and Science Van- guard Research Program, Advanced Technology Center (ATC) of NAOJ, and Mechanical Engineering Center of KEK. Software: Calibration of the LIGO strain data was performed with GstLAL-based calibration soft- ware pipeline (Viets et al. 2018). Data-quality prod- ucts and event-validation results were computed us- ing the DMT (Zweizig, J. 2006), DQR (LIGO Sci- entific Collaboration and Virgo Collaboration 2018), DQSEGDB (Fisher et al. 2021), gwdetchar (Urban et al. 2021), hveto (Smith et al. 2011), iDQ (Essick et al. 2020a), Omicron (Robinet et al. 2020) and PythonVir- goTools (Virgo Collaboration 2021) software packages and contributing software tools. Analyses in this cata- log relied upon software from the LVK Algorithm Li- brary Suite (LIGO Scientific, Virgo, and KAGRA Col- laboration 2018). The detection of the signals and sub- sequent significance evaluations were performed with the GstLAL-based inspiral software pipeline (Messick et al. 2017; Sachdev et al. 2019; Hanna et al. 2020; Cannon et al. 2021), with the MBTA pipeline (Adams et al. 2016; Aubin et al. 2021), and with the Py- CBC (Usman et al. 2016; Nitz et al. 2017; Davies et al. 2020) packages. Estimates of the noise spectra and glitch models were obtained using BayesWave (Cor- nish Littenberg 2015; Littenberg et al. 2016; Cor- nish et al. 2021). Low-latency source localization was performed using BAYESTAR (Singer Price 2016). Source-parameter estimation was primarily performed with the Bilby and Parallel Bilby libraries (Ashton et al. 2019; Smith et al. 2020; Romero-Shaw et al. 2020) using the Dynesty nested sampling package (Spea- gle 2020). SEOBNRv5PHM waveforms used in param- eter estimation were generated using pySEOBNR (Mi- haylov et al. 2023). PESummary was used to postpro- cess and collate parameter-estimation results (Hoy Raymond 2021). The various stages of the parameter- estimation analysis were managed with the Asimov li- brary (Williams et al. 2023). Plots were prepared with Matplotlib (Hunter 2007), seaborn (Waskom 2021) and GWpy (Macleod et al. 2021). NumPy (Harris et al. 2020) and SciPy (Virtanen et al. 2020) were used for analyses in the manuscript.
  • 15. 15 APPENDIX A. UPGRADES TO THE DETECTOR NETWORK FOR O4 The Advanced LIGO, Advanced Virgo, and KAGRA detectors have all undergone a series of upgrades to improve the network sensitivity in preparation for O4. In this section, we focus on upgrades made to the LIGO Livingston observatory as it was the only detector to observe GW230529; similar upgrades were made at LIGO Hanford. Some of these improvements are a part of the Advanced LIGO Plus (A+) detector upgrades (Abbott et al. 2020b). The principal commissioning work done in preparation for O4 was to enhance the optics systems in the detector. The pre-stabilized laser was redesigned for O4 with amplifiers allowing input power up to 125 W (Bode et al. 2020; Cahillane Mansell 2022). LIGO Livingston operated at 63 W in O4a. Both end test masses at LIGO Livingston were replaced because their mirror coatings contained small, point-like absorbers that limited detector sensitivity by degrading the power-recycling gain (Brooks et al. 2021). For O4, frequency-dependent squeezing was implemented with the addition of a 300 m filter cavity to rotate the squeezed vacuum quadrature across the bandwidth of the detector (Dwyer et al. 2022; McCuller et al. 2020). With frequency-dependent squeezing, uncertainty is reduced in both the amplitude and phase quadratures, allowing for a broadband reduction in quantum noise (Ganapathy et al. 2023). Squeezing was implemented independently of frequency in O3, which only reduced the quantum noise at high frequencies (Tse et al. 2019). Other commissioning work was done to improve data quality and reduce noise at low frequencies. For O4, scattered light noise was mitigated by removing some problematic scattering surfaces, and improving the resonant damping of other scatterers (Soni et al. 2020; Davis et al. 2021). Low-frequency technical noise (i.e., noise that is not intrinsic to the detector design, but can limit the detector sensitivity and performance) was reduced with the commissioning of feedback control loops, noise subtraction, and better electronics. Overall, the upgrades made during the commissioning period for O4 led to a broadband reduction in noise and improvement in detector sensitivity and performance. B. DETECTION TIMELINE AND CIRCULARS The LVK issues low-latency alerts to facilitate prompt follow-up of GW candidates (Chaudhary et al. 2023). GW230529 was initially identified in a low-latency search using data from the LIGO Livingston observatory. The candidate was given the name S230529ay in the Gravitational-Wave Candidate Event Database (GraceDB).2 After the detection of GW230529, an initial notice was sent out to astronomers through NASA’s General Coordinates Network (GCN) (LIGO Scientific, Virgo, and KAGRA Collaboration 2023a). The sky localization computed in low latency by BAYESTAR (Singer Price 2016; Singer et al. 2016) had a 90% credible area of ≈ 24200 deg2 ; the large credible area was due to GW230529 only being observed by a single detector. The initial alert also included low-latency estimates of the mass-based source classification (BNS, BBH, and NSBH) produced by the PyCBC pipeline (Villa- Ortega et al. 2022). Additional estimates that the source binary of GW230529 contained at least one neutron star, contained at least one compact object in the lower mass gap 3–5 M⊙, and had neutron-star matter ejected outside the final compact object were produced by a machine learning method trained to infer source properties from the search pipeline results (Chatterjee et al. 2020). The estimated probability that the source binary of GW230529 included at least one neutron star was 99.9%. Low-latency parameter estimation was performed with Bilby (Ashton et al. 2019; Romero-Shaw et al. 2020) and used to produce an updated sky localization and estimates of source properties sent out in another alert (LIGO Scientific, Virgo, and KAGRA Collaboration 2023b). The updated sky localization had a 90% credible area of ≈ 25600 deg2 . The updated estimate of source properties led to a slight decrease in the probability that the source binary included at least one neutron star, which was updated to 98.5%. C. QUANTIFYING SIGNIFICANCE FOR A SINGLE-DETECTOR CANDIDATE EVENT Each search pipeline has its own method for calculating the FAR of a single-detector GW candidate. In this section we will summarize these methods. 2 https://gracedb.ligo.org/
  • 16. 16 Figure 9. The noise background for the LIGO Livingston observatory collected by the GstLAL pipeline in offline mode, with the S/N–ξ2 values of GW230529 overlaid. The test statistic ξ2 measures signal consistency. The background is collected from templates that are part of the same bin as the template that recovered GW230529, and is consequently the background used to rank GW230529 and calculate its significance. The background distribution has effectively no support at the position of GW230529. The colorbar represents the probability of producing a certain S/N and ξ2 from noise triggers. C.1. GstLAL The GstLAL pipeline assigns a likelihood ratio to all of its candidate signals as the ranking statistic to estimate their significance. The likelihood ratio is the ratio of the probability of obtaining the candidate under the signal hypothesis to the probability of obtaining the candidate under the noise hypothesis. The latter probability is largely calculated by collecting S/N and ξ2 statistics of noise triggers during the analysis, where ξ2 is a signal consistency test statistic (Messick et al. 2017). Similar templates in the template bank are grouped together on the basis of the post-Newtonian (PN) expansion of their waveforms (Morisaki Raymond 2020; Sakon et al. 2024). Each template bin collects its own S/N and ξ2 statistics, which get used to rank candidates recovered by templates in that bin. Further details about the calculation of the probability of obtaining the candidate under the noise hypothesis, as well as the GstLAL likelihood ratio in general can be found in Tsukada et al. (2023). The S/N–ξ2 statistics collected from noise triggers from the same template bin as GW230529 with GW230529 superimposed are shown in Figure 9. GW230529 clearly stands out from the background, and there are no noise triggers at its position in S/N–ξ2 space. Since non-stationary noise transients known as glitches (Nuttall 2018) are not expected to be correlated across detectors, single-detector GW candidates, whether during times when a single or multiple detectors are observing, are more likely to be glitches as compared to coincident GW candidates. To account for this, the GstLAL pipeline downweights the logarithm of the likelihood ratio of single-detector candidates by subtracting an empirically-tuned factor of 13, which is optimized to maximize the recovery of candidates with an astrophysical origin while minimizing the recovery of glitches (Abbott et al. 2020a). The FAR of the GstLAL pipeline for GW230529 quoted in Table 1 is calculated after the application of this penalty. Finally, the FAR for a candidate in the search is computed by comparing its likelihood ratio to the likelihood ratios of noise triggers not found in coincidence, after accounting for the live-time of the analysis. These noise triggers not found in coincidence allow the pipeline to extrapolate the background distribution of likelihood ratios to large values, enabling the inverse FAR of a candidate to be greater than the duration of the analysis. While in the low-latency mode, the GstLAL FAR calculation uses the background from the start of the analysis period until the time of the candidate. In contrast, for its offline analysis, the GstLAL pipeline uses background collected from the full analysis period including the entirety of O4a to rank candidates. This differs from the other search pipelines presented in this work which only use background from the first two weeks of O4a for their offline search results presented here. The GstLAL offline analysis was performed using the same template bank as the online analysis (Sakon et al. 2024; Ewing et al. 2023). Details are liable to change for future offline GstLAL analyses in O4a. However, for such a
  • 17. 17 Figure 10. Ranking statistic distribution of MBTA single-detector triggers in the LIGO Livingston observatory during the first two weeks of O4, excluding significant public alerts aside from GW230529. significant candidate as GW230529, we do not expect these changes to impact its interpretation as highly likely being of astrophysical origin. C.2. MBTA The MBTA single-detector candidate search for O4a focuses on a subset of the full MBTA parameter space. The goal is to focus on BNS and NSBH signals, which are most interesting because of their rarity and possible EM counterparts. Their long signal duration also makes them easier to identify and allows for a better sensitivity to be reached when compared to a single-detector candidate search using the whole MBTA parameter space. The parameter space for the O4a online single-detector search was defined based on the detector-frame (redshifted) primary mass and chirp mass of the templates and motivated by the computation of the probability for whether a non-zero amount of neutron star material remained outside the final remnant compact object (Chatterjee et al. 2020) introduced in Appendix B. The considered space is (1 + z) m1 50 M⊙ and (1 + z) M 5 M⊙ (Juste 2023). For the offline analysis, this space was adapted and we consider only (1 + z) M 7 M⊙. MBTA online also applied selection criteria based on data-quality tests to its single-detector candidates (Juste 2023). This was changed to a reweighting of the ranking statistic for the offline analysis. The ranking statistic for MBTA single-detector triggers is a reweighted S/N. The reweighting is based on the computation of a quantity called auto χ2 (Aubin et al. 2021), which tests the consistency of the time evolution of the S/N time series. The additional reweighting used in the offline analysis relies on the computation of a quantity that identifies an excess of S/N for single-detector triggers. The excess of S/N is larger for triggers that have a noise origin compared to astrophysical signals or injections, and therefore allows for discrimination between astrophysical signals and noise. The ranking statistic distribution of the MBTA offline analysis for single-detector triggers during the first two weeks of O4a is shown in Figure 10. Other triggers which produced significant public alerts have been removed from the plotted distribution. GW230529 stands out from the background with a high ranking statistic that reflects the auto χ2 value being completely consistent with a signal origin. The FAR in MBTA is a function of pastro (Andres et al. 2022), the probability of astrophysical origin of the candidate. It is derived from the combined parametrizations of the FAR as a function of the ranking statistic and of pastro as a function of the ranking statistic. Inverting the latter gives the ranking statistic as a function of pastro and eventually the FAR as a function of pastro. The background estimation for MBTA single-detector triggers was computed differently during the online and offline analyses. The online analysis relies on the computation of simulated single-detector triggers obtained through random combinations of single frequency-band data (Juste 2023). O4a online analysis and the method of randomly combining single-frequency band data showed that the background for MBTA single-detector triggers follows an exponential distribution and is stable in time beyond statistical fluctuations. This prompted us to update the model we use for the offline (and future) analyses to reach greater sensitivity. This new model involves extrapolating the observed distribution of single-detector triggers and removing the significant triggers.
  • 18. 18 Figure 11. Ranking statistic distribution of PyCBC offline single-detector triggers in the LIGO Livingston observatory during the first two weeks of O4. The plotted distribution may include triggers from other less-significant signals arriving during the period analyzed. A safety margin is used in the extrapolation such that the FAR is over-estimated relative to the best-fit extrapolated distribution. This change in methods, in addition to the difference in handling of single-detector triggers online and offline, explains the difference in inverse FAR for the online (1.1 yr) and offline (1000 yr) analyses. C.3. PyCBC In PyCBC, each GW candidate is assigned a ranking statistic, and then a FAR is calculated by comparing the ranking statistic of the candidate to the background distribution. The details of this procedure differ between the online and offline versions of the PyCBC search. In the online pipeline, we consider single-detector candidates only from templates with duration greater than 7 s above a starting frequency of 17 Hz, corresponding to a range of masses and spins for which EM emission due to neutron star ejecta might be expected. Low-latency data quality timeseries produced by iDQ, a machine learning framework for autonomous detection of noise artifacts using only auxiliary data channels insensitive to GWs (Essick et al. 2020a), are used to veto candidates at times when a glitch is likely to be present in the data. The remaining single-detector candidates are ranked by the reweighted S/N described in Nitz (2018). Only candidates with a χ2 statistic (Allen 2005) 2.0 and reweighted S/N 6.75 are kept. The rate density of single-detector triggers above the reweighted S/N threshold is fit with a decreasing exponential. In offline PyCBC, we only consider single-detector candidates from templates with duration greater than 0.3 s above a starting frequency of 15 Hz. We also require that candidates have a χ2 statistic 10.0, a reweighted S/N 5.5, and a PSD variation statistic (Mozzon et al. 2020) 10.0, in order to exclude high-amplitude noise transients. Each candidate is assigned a ranking statistic equal to the logarithm of the ratio of astrophysical signal likelihood to detector noise likelihood. The PyCBC O4 offline search introduced two changes to the ranking statistic relative to the O3 calculation. First, an explicit model of the signal distribution covering the space of binary masses and spins is included (Kumar Dent 2024). The model is designed to maximize the number of detected signals from the known compact binary distribution, while also maintaining sensitivity to signals in previously unpopulated regions. Second, the model of the rate density of events caused by detector noise now includes a term describing the variation in rate during times of heightened detector noise (Davis et al. 2022). The rate density of single-detector candidates above a ranking statistic threshold of 0 is fit with a decreasing exponential. In both the online and offline versions of PyCBC, the exponential fit of trigger rate density above the relevant ranking statistic threshold is used to extrapolate the FAR of single-detector candidates beyond the observing time of the search (Cabourn Davies Harry 2022). The FAR calculations for GW230529 used triggers from the first two weeks of O4 at the LIGO Livingston observatory. The distribution of ranking statistics for offline single-detector candidates at the LIGO Livingston observatory is shown in Figure 11. Similar to the other searches, GW230529 clearly stands out from the background distribution.
  • 19. 19 Table 4. Summary of parameter-estimation analysis choices for GW230529, and the physical content of each waveform model used. Here, tides refers to modeling of neutron star tidal deformability and disruption when tidal forces overcome the self-gravity of the neutron star. The spin prior denotes any restrictions on the spin magnitude of the binary components. Waveform Model Precession Higher Multipoles Tides Disruption Spin Prior IMRPhenomNSBH − − ✓ ✓ χ1 0.50, χ2 0.05 IMRPhenomPv2 NRTidalv2 ✓ − ✓ − χ1 0.99, χ2 0.05 IMRPhenomXPHM ✓ ✓ − − χ1 0.99, χ2 0.99 SEOBNRv5PHM ✓ ✓ − − χ1 0.99, χ2 0.99 SEOBNRv4 ROM NRTidalv2 NSBH − − ✓ ✓ χ1 0.90, χ2 0.05 IMRPhenomXPHM ✓ ✓ − − χ1 0.99, χ2 0.05 IMRPhenomXP ✓ − − − χ1 0.99, χ2 0.99 IMRPhenomXHM − ✓ − − χ1 0.99, χ2 0.99 IMRPhenomXAS − − − − χ1 0.99, χ2 0.99 IMRPhenomXAS − − − − χ1 0.50, χ2 0.05 IMRPhenomPv2 NRTidalv2 ✓ − ✓ − χ1 0.05, χ2 0.05 IMRPhenomXPHM ✓ ✓ − − χ1 0.05, χ2 0.05 SEOBNRv5PHM ✓ ✓ − − χ1 0.99, χ2 0.05 D. PRIORS, WAVEFORM SYSTEMATICS, AND BAYES FACTORS Given the uncertain nature of the compact objects, we analyze GW230529 with a suite of models that incorporate a number of key physical effects. The choices of data duration (128 s) and frequency bandwidth (20–1792 Hz) analyzed were informed by comparing waveforms spanning the mass range recovered in preliminary analyses to the detector noise PSD at the time of the event. The high-frequency cutoff is chosen to avoid loss of power at high frequencies due to low-pass filtering of the data. For a subset of the signal models below, we employ a range of techniques to speed up the evaluation of the likelihood including heterodyning (also known as relative binning; Cornish 2010; Zackay et al. 2018; Cornish 2021; Krishna et al. 2023), multibanding (Garcı́a-Quirós et al. 2021; Morisaki 2021), and reduced order quadratures (Canizares et al. 2015; Smith et al. 2016; Morisaki et al. 2023). The physical effects included and the spin prior ranges for each waveform model considered in this work are shown in Table 4. All analyses use mass priors that are flat in the redshifted component masses with chirp masses, M = (m1m2)3/5 /(m1 +m2)1/5 ∈ [2.0214, 2.0331] M⊙ and mass ratios q ∈ [0.125, 1]. The luminosity distance prior is uniform in comoving volume and source-frame time on the range DL ∈ [1, 500] Mpc. The priors on the tidal deformability parameters are chosen to be uniform in the component tidal deformabilities over Λ ∈ [0, 5000]. Standard priors (e.g., Romero-Shaw et al. 2020; Abbott et al. 2024b) are used for all the other extrinsic binary parameters. Below we provide further motivation for considering this suite of waveform models. The primary analysis in this work uses the IMRPhenomXPHM and SEOBNRv5PHM BBH waveform models (corre- sponding to the third and fourth rows in Table 4), which provide an accurate description of BBHs but do not incorporate tidal effects or the potential tidal disruption of a companion neutron star. We did not consider an extension of IMR- PhenomXPHM that incorporates additional physics beyond the two precessing higher-order multipole moment BBH models used here as these effects only enter at high frequencies and are not relevant for this event (Thompson et al. 2024). In order to quantify the impact of neglecting tidal physics, we analyze GW230529 with NSBH and BNS wave- form models that incorporate different tidal information. The NSBH models only incorporate tidal information from the less massive compact object, are restricted to spins aligned with the orbital angular momentum, and only model
  • 20. 20 the dominant ℓ = m = 2 multipole moment. However, they do model the possible tidal disruption of the neutron star, which occurs when tidal forces of the black hole dominate over the self-gravity of the neutron star. We use two NSBH models, a frequency-domain phenomenological model IMRPhenomNSBH (Thompson et al. 2020a), and a frequency-domain effective-one-body surrogate model SEOBNRv4 ROM NRTidalv2 NSBH (Matas et al. 2020). IMRPhenomNSBH uses the BBH models IMRPhenomC (Santamaria et al. 2010) and IMRPhenomD (Husa et al. 2016; Khan et al. 2016) as baselines for the amplitude and phase, respectively, incorporating corrections to the phase due to tidal effects following the NRTidal model (Dietrich et al. 2017, 2019b,a) and to the amplitude following Pannarale et al. (2013, 2015). SEOBNRv4 ROM NRTidalv2 NSBH uses the SEOBNRv4 BBH model as a baseline (Bohé et al. 2017) and applies the same corrections to account for tidal deformability and disruption as IMRPhenomNSBH but is additionally calibrated against numerical relativity (NR) simulations of NSBH mergers (Foucart et al. 2013, 2014, 2019; Kyutoku et al. 2010, 2011). As the NSBH waveform models do not capture spin-induced orbital precession, we analyze GW230529 with the aligned-spin BBH waveform models IMRPhenomXAS (Pratten et al. 2020), which only contains the dominant harmonic, and IMRPhenomXHM (Garcı́a-Quirós et al. 2020), which includes higher-order multipole moments. Models for NSBH binaries that contain both higher-order multipole moments and precession are under active development (Gonzalez et al. 2023) and could potentially allow for a more consistent model selection between the different source categories. Given that the mass of the primary overlaps with current estimates of the maximum known neutron star mass (Landry Read 2021; Romani et al. 2022), we also analyze GW230529 with a BNS waveform model that allows for tidal interac- tions on both the primary and the secondary components of the binary. We use IMRPhenomPv2 NRTidalv2 (Dietrich et al. 2019a), which adds a model for the tidal phase that is calibrated against both effective-one-body (EOB) and NR simulations to the underlying precessing-spin point-particle waveform model IMRPhenomPv2 (Hannam et al. 2014). A limitation is that IMRPhenomPv2 NRTidalv2 is calibrated against a suite of equal-mass, non-spinning BNS NR simulations, where the maximum neutron star mass is only 1.372 M⊙. Nevertheless, the model has been validated against a catalog of EOB–NR hybrid waveforms that includes asymmetric configurations and heavier neutron star masses (Dietrich et al. 2019a; Abac et al. 2024). Because of large uncertainties in BNS postmerger waveform modeling, IMRPhenomPv2 NRTidalv2 includes an amplitude taper from 1–1.2 times the estimated merger frequency (Dietrich et al. 2019b). The resulting suppression of S/N at these frequencies may be responsible for the posterior differences between IMRPhenomPv2 NRTidalv2 and the BBH and NSBH waveform models we consider (see Figure 12). From the mass estimates alone, the secondary object is consistent with being a neutron star. As such, we follow earlier analyses and analyze GW230529 with two spin priors (Abbott et al. 2021a): an agnostic high-spin prior and an astrophysically motivated low-spin prior. The high-spin prior assumes that the spins on both objects are isotropically oriented and have dimensionless spin magnitudes that are uniformly distributed up to χ1, χ2 ≤ 0.99. The low-spin prior, on the other hand, is inspired by the extrapolated maximum spin observed in Galactic BNSs that will merge within a Hubble time (Burgay et al. 2003; Stovall et al. 2018), and restricts the spin magnitude of the secondary to be χ2 ≤ 0.05 while keeping χ1 ≤ 0.99. As the nature of the primary as a black hole or neutron star is uncertain, we also use a third choice of prior where both spins are restricted to χ1, χ2 ≤ 0.05 for the IMRPhenomPv2 NRTidalv2 and IMRPhenomXPHM waveform models (rows 11 and 12 of Table 4, respectively). The purpose of using multiple priors is to help gauge whether astrophysical assumptions on the neutron star spin impact any of the statements on the probability that the primary object lies in the lower mass gap. In Figure 12, we show the impact of waveform systematics and prior assumptions on the strongly correlated mass ratio–effective inspiral spin distribution. The degree to which a given waveform model under certain assumptions matches the data can be gauged using the Bayes factor. However, Bayes factors penalize extra degrees of freedom in models that do not improve the fit when those extra degrees of freedom are constrained by the data (Mackay 2003). We find no significant preference (log10 B ≲ 0.5) between the high-spin and low-spin prior on the secondary; we similarly do not find a statistical preference for or against the effects of precession, higher-order multipole moments, or tidal deformation or disruption of the secondary object. E. ADDITIONAL SOURCE PROPERTIES E.1. Component Spins and Precession Assuming a high-spin prior, the posteriors for the primary spin magnitude are only weakly informative, disfavoring zero and extremal spins with χ1 = 0.07–0.85. For the secondary, the posteriors are even less informative. Under the low-spin prior, the primary spin magnitude posterior is peaked at slightly higher values with zero and extremal
  • 21. 21 Figure 12. The two-dimensional q–χeff posterior probability distributions for GW230529 using various BBH, NSBH, and BNS signal models. The vertical dotted lines indicate primary masses that have been mapped to the mass ratio given the median chirp mass estimated from the IMRPhenomXPHM high-spin analysis. spins being disfavored to a larger degree, χ1 = 0.10–0.84. The secondary spin is completely uninformative over the restricted range of spin magnitudes. The joint two-dimensional posterior probability distribution of the dimensionless spin magnitude and the spin tilt are shown in Figure 13. Regions of high (low) probability are denoted by a darker (lighter) shade. When the spins are misaligned with the orbital angular momentum, relativistic spin-orbit and spin-spin couplings drive the evolution of the orbital plane and the spins themselves (Apostolatos et al. 1994; Kidder 1995). The leading- order effect can be captured by an effective precession spin parameter, 0 ≤ χp ≤ 1, which approximately measures the degree of in-plane spin and can be used to parameterize the rate of precession of the orbital plane (Schmidt et al. 2015) χp = max χ1 sin θ1, 3 + 4q 4 + 3q q χ2 sin θ2 . (E1) We find the constraints on χp to be uninformative, and we are not able to make any significant statements on precession. The uninformative nature of these results is corroborated by the Bayes factor between the precessing and non-precessing phenomenological waveform models, log10 BXP XAS = 0.22. E.2. Source Location and Distance As GW230529 was a single-detector observation, the sky localization is poor and covers a sky area of ≈ 24100 deg2 at the 90% credible level. The luminosity distance is inferred to be DL = 201+102 −96 Mpc, corresponding to a redshift of z = 0.04+0.02 −0.02 computed using the Planck 2015 cosmological parameters (Ade et al. 2016). The luminosity distance has a degeneracy with the inclination angle of the binary’s total angular momentum with respect to the line of sight, θJN (e.g., Cutler Flanagan 1994; Nissanke et al. 2010; Aasi et al. 2013; Vitale Chen 2018). The posterior distribution on θJN is broadly unconstrained, showing no preference for a total angular momentum vector that is pointed towards or away from the line of sight. E.3. Tidal Deformability The tidal deformability of a neutron star is defined by λ = 2 3 k2R5 , (E2)
  • 22. 22 Figure 13. Two-dimensional posterior probability distributions for the spin magnitude χi and the spin-tilt angle θi for the primary (left) and secondary (right) compact objects at a reference frequency of 20 Hz. A spin-tilt angle of 0◦ (180◦ ) indicates a spin that is perfectly aligned (anti-aligned) with the orbital angular momentum L̂. The pixels have equal prior probability, and shading denotes the posterior probability of each pixel of the high-spin prior analysis, after marginalizing over azimuthal angles. The solid (dashed) contours denote the 90% credible region for the high-spin (low-spin) prior analyses respectively. The probability distributions are marginalized over the azimuthal spin angles. where k2 is the gravitational Love number of the object and R is its radius (Damour et al. 1992; Mora Will 2004; Flanagan Hinderer 2008; Damour Nagar 2009). However, it is often convenient to introduce a dimensionless tidal deformability Λ = λ m5 = 2 3 k2C−5 , (E3) where C = m/R is the compactness of the neutron star in geometrized units. Using the IMRPhenomPv2 NRTidalv2 model, which allows for tidal deformability on both objects but does not model tidal disruption, we infer Λ1 ≤ 1462 at 90% credibility with the χ1 0.99, χ2 0.05 spin prior; the posterior peaks at Λ1 = 0. We do not constrain Λ2 relative to the prior. Constraints on the tidal deformability Λ of both components of GW230529 are shown in Figure 14, along with the tidal deformabilities predicted for the secondary object under the BSK24 neutron star EoS (Goriely et al. 2013; Pearson et al. 2018; Perot et al. 2019) and using the Gaussian process (GP)-EoS constraints introduced in Section 6. BSK24 is chosen as an illustrative EoS that is thermodynamically consistent and falls within the range of support of constraints from nuclear physics and astrophysics, including GW170817. The uninformative Λ2 posterior is consistent with both of these predictions. In addition to the tidal deformability posteriors, we use two distinct likelihood interpolation schemes (Ray et al. 2023a; Landry Essick 2019) to directly constrain the neutron star EoS using both spectral (Lindblom 2010; Lindblom Indik 2012, 2014) and GP (Landry Essick 2019; Essick et al. 2020b) representations. Both methods incorporate consistency with the observed heavy pulsars PSR J0740+6620 (Fonseca et al. 2021) and PSR J0348+0432 (Antoniadis et al. 2013) as priors on the EoS and enforce thermodynamic stability and causality. Unlike other analyses where the GP representations are conditioned on both GW and pulsar data, here we only include the pulsar constraints in the prior, in order to distinguish the EoS information provided by GW230529 alone. These direct EoS inferences are also uninformative, returning their respective priors.
  • 23. 23 Figure 14. Constraints on dimensionless tidal deformability Λ for the primary (green dashed) and secondary (green solid) components of GW230529. We also show tidal deformabilities predicted for the secondary object under the BSK24 neutron star EoS (navy; Goriely et al. 2013; Pearson et al. 2018; Perot et al. 2019) and constraints obtained from BNS and pulsar observations using the GP model (GP-EoS; red). F. TESTING GENERAL RELATIVITY To verify whether GW230529 is consistent with general relativity, we perform parameterized tests searching for deviations in the PN coefficients that determine the phase evolution of the GW signal (Blanchet Sathyaprakash 1994, 1995; Arun et al. 2006a,b; Yunes Pretorius 2009; Mishra et al. 2010; Li et al. 2012a,b). Specifically, we search for parametric deviations to the GW inspiral phasing applied to the frequency-domain waveform models IM- RPhenomXP NRTidalv2 (Colleoni et al. 2023) and IMRPhenomXPHM (Pratten et al. 2020; Garcı́a-Quirós et al. 2020; Pratten et al. 2021) using the TIGER framework (Agathos et al. 2014; Meidam et al. 2018), and SEOB- NRv4 ROM NRTidalv2 NSBH (Matas et al. 2020) and SEOBNRv4HM ROM (Bohé et al. 2017; Cotesta et al. 2018, 2020) using the FTI framework (Mehta et al. 2023a). These waveform models each capture different physical effects (precession, higher-order multipole moments, and neutron star tidal deformability) to determine whether their absence in the model leads to inferred inconsistencies with general relativity. For all waveform models and PN orders whose analyses have been completed, we find that GW230529 is consistent with general relativity within the inferred uncertainties on the deviation parameters. We do not yet include results about 0PN deviations, which are being examined separately due to technical issues related to the degeneracy between the 0PN deviation parameter and the chirp mass (Payne et al. 2023). The constraints obtained at −1PN are an order of magnitude tighter than previously reported bounds for NSBH and BBH (Abbott et al. 2021b). The previously reported bounds using GW170817 remain the tightest constraints on −1PN deviations obtained with GWs (Abbott et al. 2019c). Further details about the tests of general relativity performed will be presented in a follow-up paper. G. COMPACT BINARY MERGER RATES METHODS A key component of the event-based rate estimation described in Section 5 is the sensitive time–volume of our GW searches. The sensitivities to GW200105-, GW200115-, and GW230529-like events are computed from O1 through the first two weeks of O4a according to the corresponding mass and spin posteriors from the IMRPhenomXPHM high-spin analyses of these signals. The posterior samples chosen for this analysis are consistent with previous event-based rate estimates presented for NSBH mergers (Abbott et al. 2021a). Simulated signals, whose binary parameters are drawn from the mass and spin posteriors for each signal, are distributed uniformly in comoving volume and following the other extrinsic parameter distributions given in Appendix D, and are added to simulated detector noise characterized by representative PSDs for each observing run. The detectability of these injections is then calculated semi-analytically to determine the sensitive time–volume by calculating network responses to the simulated signals and applying a threshold on the network optimal S/N of 10. This choice of threshold was previously tuned to the results of matched filter searches (Abbott et al. 2021c), and is comparable to threshold statistics calculated for semi-analytic sensitivity estimates (Essick 2023).